Can anyone recommend some restaraunts that are reasonably priced near the Intercontinental?
Define reasonably priced. But too many to list, you're in the heart of a city with the top-notch public transport.
But you might as well get a bit more around, visit Petrus, Két Szerecsen, Rosenstein (don't miss this one), Kispiac. By local standards, these are more upmarket and are casual fine dining places, but Borkonyha, Olimpia, Stand25, Innio, Csalogány26 all deserve a visit as well, the first 3 being my favorites.
note that Stand25 is just that -- a 'stand' (actually a small but open enclosure in a converted market hall that now basically sells high end fast food and takeaway and a bit of sit-down eating) -- and is not comparable in setting to any of the others. On the other hand, it is owned and operated by the first two Michelin-starred chefs in Hungary -- they husband and wife team who brought Onyx's first star to Budapest, Tamas Széll and Szabina Szulló. And it has a Bib Gourmand. But it is not really a restaurant and its effort to be one (by serving dinner weekend evenings) is kind of creepy because the entire rest of the venue is pretty much deserted.