Unfortunately, I am afraid that most natural beauties are not easily accessible using a wheelchair. Surely there are some natural attractions such as Strbske Pleso, the second largest tarn in High Tatras, that can be directly seen from the sidewalk surrounding it, but for many other destinations it won't be that easy. :(
I mean, for example High Tatra mountains can be surely visited even by handicapped person in a wheelchair, because there is a relatively good infrastructure with a lot of top quality hotels or restaurants, which feature barrier-free access; and, of course, a really beautiful sightseeings of High Tatras can be seen even from places nearby roads and sidewalks, but those true natural attractions can by reached only after hours of walking tourist-paths, usually deep in the forests. Naturally, those are far from being considered as a barrier-free access.
However, there are also a lot of non-natural or partially natural attractions in Slovakia that I definitely suggest you to visit, such as: historical UNESCO towns, open-air museums showcasing traditional lifestyle from past centuries (skansens) or even some castles that can be at least partially accessible using a wheelchair.
Also, I believe that even the Lomnicky Peak, one of the highest and most visited mountain peaks in the High Tatra mountains can be visited by a wheelchair, because there are cable-railways leading right to the top of it; but even after some time of Googling now, I am still unsure about whether is it actually possible. :/
Anyway, here are some skansens that are at least partially accessible using a wheelchair.
Great place to spend the night is this medieval castle, renovated to the top quality hotel:
There are also some expositions right in the castle showcasing its history. This castle is really a great place to visit, eat, drink and spent the night. ;)
If you like water, swimming and relax you may want to visit:
Is is the biggest aqua-park in central Europe with thermal water.
Surely, it is not tourist attraction in terms of country's history, but anyway, you may enjoy it as a place to stop-by on your way.
Anyway, I suggest you to check this interactive map. There are really the best tourist-attractive places enlisted, basically places, which I would suggest you, thus if you choose from there you cannot go wrong. The only disadvantage of that map is that it doest sort destinations by barrier-free access. I realize it is a big problem in this specific case, but anyway that map and website is probably the best what you can find, when you are planing your trip(s).
If you have more questions, feel free to ask. :)