Here are the places I’d recommend for excellent strudel and hot chocolate in Budapest:
Zholnay Kavehaz (V. kerület, Váci u. 20) is a lovely place where tasty pastries can be found at reasonable prices. It is located few steps away from the Hotel Taverna and offers a lot of mouth-watering dishes. Here you can find one of the best Viennese strudels covered with hot vanilla sauce. Or try something else like hot chocolate or apricot cheesecake.
Rózi Néni Rétesei (Mester utca) is not a café and looks more like a street kiosk. But if you happen to be nearby, make a point of visiting this family owned place. It serves one of the best strudels in all Budapest. They are based on an old family recipe. You can find thirteen different kinds of sweet and savory strudels. And the price will make you happy – only about 1 dollar per portion. Keep in mind that lines are long in the morning, so arrive early.
Café Ruszwurm is a very famous and old place in the Buda part of the city. It is a confectionery that offers many tasty things, but strudels here are especially fantastic. Fillings include sour cherry, farmers cheese, poppy seed, or apple.
Cafe Cicero (V. Oktober 6. u. 19.) is a small family run café-restaurant. It is very clean and has nice service. Breakfasts are available in here all day long as well as delicious hot chocolate and various pastries. If you arrive in winter, it is the best location to warm up and have good meals. Full breakfast will take you near 6$ and a cup of home made and extremely hearty hot chocolate with or without spices nearly 1-2$.
Aztek Chocolat (V. Károly krt. 22) is the perfect place to indulge in really good coffee and, especially, hot chocolate. There are several varieties of hot chocolate on the menu, including a dark chocolate one with Mexican chili for that extra kick. A large one will cost you nearly $3, but you can have it instead of breakfast!