Thank you for the question and the answer is yes. Most shops, restaurants and activities in Budapest accept payment with VISA card.
There are of course some exceptions to the rule, especially in smaller restaurants (like Comme Chez Soi) and if you visit Szentendre most shops there only accept payment in cash. However the general “rule” is that shops in the shopping street Vaci utca, shops in the malls and so on accept payment with VISA.
The Great Market Hall, a very popular place to go shopping, does not accept payment with VISA on any of the stands on the inside, so before entering this traditional market place downtown Budapest you better prepare yourself with some Hungarian Forint.