Oh I love Budapest for its butcher shops (and so do Budapest building workers as I’ve noticed)! Not only can you shop there but you can certainly eat, yep! It’s damn cheap and tasty, well… if you’re not vegetarian!
Grilled sausage (kolbász), frankfurters, grill chicken, meat-brochettes… at Pinczi’s, just a few meters away from Nyugati railway station (caution though it’s getting hidden by a big Kekab shop next door), you’re pretty sure you won’t miss the point, anytime during the day till it closes (quite early).
Just do as the Romans do here: eat with your hands from a paper plate heavily recovered with local mustard (nothing to do with the original Dijon product, it tastes more like its American substitute!). Homemade French fries are available if you go there early enough (till 13:00 usually). You can also try all sorts of pickles and have a bite in the super fluffy Magyar bread baked with its own label on it!
You can get drinks – including vodka less than 200 Ft, never tried it though! – and even wash your hands (you’ll need it!).
Don’t expect too much English to be spoken but the staff is nice so just make some gestures and smiles to show what you want!