This app was mentioned in 14 comments, with an average of 2.43 upvotes
it is legal to do so, it's just very rare for people to do that. You can usually find some off-road path suitable for horse riding(check mapy.cz https://play.google.com/store/apps/details?id=cz.seznam.mapy )
Die App Mapy.cz kann sowas soweit ich weiß. Ich habs aber noch nicht ausprobiert, kann also nicht sagen, wie die Qualität ist. Google Play
Én a Mapy.cz appal szoktam biciklire tervezni, a bartókos, körúti, stb. bringasávok mind benne vannak. A merretekerjekhez képest nem tudom, mennyire gyakran frissített, de kicsit talán felhasználóbarátabb.
Anno egy prágai ismerősöm ajánlotta, és meglepően jó Budapestre is.
By the way, an app I've been using both on web and on phone for years is now in English and uses OpenStreet maps for "rest of the world". You can download specific countries for free. It also has the nicest renderer out there (in my opinion) and includes lots of POI. It's missing good aerial data and street view.
I really recommend you give it a try. I mostly use it in their home country so the data there are excellent, but I've used it in Germany as well and it worked just fine. You can create routes online and save them to see on the phone (needs account) which is nice since the phone interface isn't that great for route building if you want to avoid hills and such. It also can record routes, but I haven't tried that. Works as navigation as well I think, I only use maps with lines and do the navigation myself.
Since no one mentioned it yet, let me cover Slovenský Raj.
Useful links:
A website of the national park - bit minimalistic as far as webdesign goes, but it does have useful info in english.
Hiking map of the area - unfortunately it's in Slovak, but still useful.
Android or IOS app for offline hiking maps. Not sure about language options, but still useful when out in the woods with spotty internet connection.
When going hiking you should buy a ticket - they are fairly cheap (1.5€ for a person a day, the price can go down for stuff like multi-day tickets, children etc.) and can be bought at most entrances into the park itself. One thing to keep in mind when hiking in the Slovak Paradise is that almost all the canyon trails are one way, from bottom to top. Also, if you have problems with heights, they may not be for you, though I find that they can help in that regard - exposure being a decent therapy and all that.
Probably the most visited trail is Suchá Belá. It is quite beautiful, but usually very crowded. It starts in Podlesok, follows the green trail up the canyon and then the yellow and red trail down.
Personally I am quite fond of the Prielom Hornádu - Kláštorná Roklina hike. Again start in Podlesok, follow the blue trail through Prielom until you reach the crossroads at the big bridge and then go up through a canyon on the green trail. From that point you can either go back down on the green trail, or if you want more you can go further on the blue trail towards Malý / Veľký Kyseľ.
There's also Via Ferrata Kyseľ if you want something a bit more action packed, though to be honest it is quite easy as far as ferratas go. You can either start at Čingov and follow the blue then green trail or start at Podlesok and follow the red trail to Kláštorisko and then go down through the yellow trail. You will need to buy a separate ticket for it and you'll need to rent the safety equipment, but they sell/rent those at both those starting points. If you want you can combine this with the Prielom hike I mentioned.
On the western side you have two more canyons - Piecky and Veľký Sokol. Píla is a good starting point for those two.
For light stuff there's Zejmarská roklina in the south part of the national park, the hike starts at in Dedinky or Tomášovský výhľad from Čingov in the north-east.
There's more but these should cover the basics.
Mapy.cz, a map portal by Czech search company Seznam also uses OSM for areas outside fo Czech Republic and their app allows you to download individual countries for offline use ("tourist" layer with bike paths and such, all free). The app is pretty good and has a much nicer renderer compared to other OSM apps I've tried.
It only has online routing I believe (car, bike, walk), but you can upload, create&save and record routes. It has bunch of nice features (single-finger zoom!, first aid), but it is pretty czecho-centric... so.. try before relying on it I guess.
Tačnije u kom pogledu?
Imaš OpenStreetMap, samo što je to čitav ekosistem, tako da treba naći konkretnu aplikaciju za tvoje potrebe koja je bazirana na tim podacima. Za rutiranje koristim https://maps.openrouteservice.org. Za opštu upotrebu na telefonu je mapy.cz vjerovatno najbolja aplikacija koja ima.
>Hiking in Buda Hills looks really nice but we are going to be dependent on public transport, so will it be easy for us to get there?
Yes pretty easy. You can rely on Google Maps for planning routes with public transport, it's pretty good.
I recommend the cogwheel railway (fogaskerekű vasút), nowadays called tram 60, to get up the hills. Much nicer experience than taking the bus. Normal Budapest travel passes are valid on it, there is no extra charge. However, there is an extra charge for the chairlift (Libegő) and the Childrens' Railway (gyermekvasút), but it's not that expensive.
For hiking routes, you can check out these maps:
https://en.mapy.cz/turisticka?x=18.9634872&y=47.5062126&z=13
https://tervezo.heyjoe.hu/#14/47.5209/18.9835/opentopo-turajel
For android phones, I suggest the Mapy.cz app (don't forget to switch the map to "outdoor" so it shows marked trails highlighted with their color:
https://play.google.com/store/apps/details?id=cz.seznam.mapy&hl=en&gl=US
This is a nice hike from the cogwheel railway to Hűvösvölgy, from there you can take a tram back to the city. It takes approx 3 hours, there are 3 lookout towers on the way:
https://en.mapy.cz/s/bagukodape
If it is too long, it is a good variant to check out the lookout tower at Point 2, then walk back to the top station of the chairlift and then take the chairlift to the bottom station. (There is a bus from there back to the city). Whatever you do, if you take the chairlift, organize the trip so that you take the chairlift down from the hill, not up. You get much better views then, you will be looking at the city. If you take it to get to the top, you will be looking at the ground in front of you the whole time.
Another popular route if you want to minimize walking and maximize fun/unusual ways of transportation: Take the Fogaskerekű (cogwheel railway) to the top, then take Gyermekvasút (childrens' railway) to Jánoshegy station, from there walk up to the peak of János-hegy, check out the lookout tower, then take the Libegő (chairlift) down to the valley.
I think this app is the best.
I can't recommend Mapy.cz for hiking trips enough. Google Maps for "not in the city" navigation just sucks. Play Store link
én ezt ajánlom: Mapy.cz
Nem csak magyar, hanem kb sok ország offline is letölthető turistatérképei
https://play.google.com/store/apps/details?id=cz.seznam.mapy&hl=en&gl=US
For Europe offline navigation I would recommend mapy.cz You can save any part of the world offline for free.
Example route: Start of Kungsleden trail in Sweden.
It's a derivative of an older app mapy.cz which is targeted to people in Czech Republic and Slovakia (and is massively popular there).
You can check their app.
They use OpenStreetMap data for countries other than the Czech Republic.