I have been to Bucharest.
It is not in the same league as many of the other big cities in Europe, I think.
Not a lot of tourist attractions.
A bit shabby in places.
But for your purposes, it might fit the bill.
I found it an interesting city not very geared towards tourism and was perfectly happy there and am going back later this year.
It certainly has interesting and impressive buildings, not least the enormous palace of the parlament.
It has an old town, not big as part of it was torn down to build the parlament.
It would have hotels that are cheap. I stayed in the Hilton Athenee Palace which is in a lovely building and is a very nice hotel ( nice breakfast ).
And it certainly has good food at very reasonable prices.
If you go, this restaurant is a must ( try the spoon tasting ) :
http://theartist.ro
I also had very nice beef several places ( can only remember these two places):
http://www.vacamuuu.com
http://oshoprimaverii.ro
And I am sure there are markets. I cannot recommend any as I don't remember if I went to any ( I normally do ). It was frightfully cold when I was there and I could have skipped this enjoyment.