I'll assume these are all new places for you.
As another single male, I'd go to Budapest. But I haven't been to Talinn. And I'd probably skip Bratislava. Maybe cut Budapest to 4 days and do 2 somewhere else. If you stick with Bratislava, one day is enough.
Budapest is probably my favorite city in Europe. As you said, relatively cheap compared to just about everywhere to the west of it. Very good food, including some Michelin-starred restaurants which are affordable (relative to others elsewhere). The ruin pubs are fun and quirky. Good Hungarian wine, good beer everywhere in the city. Beautiful views, both looking across the river from the Pest side and from Castle Hill looking back at Pest. Enough interesting sight seeing to keep you occupied during the day if you haven't been there before. The baths are an interesting and, once you get used to it, relaxing experience. The Great Market Hall is a great place to walk around for 30 minutes and then get some really good lunch for cheap.
But all of that depends on what your interests are when you travel. Mainly I think I like that Budapest feels like a real European city even in the hotel area along the Danube instead of just a big tourist attraction.
I'm actually going back in August. One of my to-do's that I learned about recently and didn't get a chance to do last time is eat at a butcher shop. Google it, if you're into food at all, it looks fantastic. The other new thing on my list is visiting the Terror Museum.
All that said, Tallinn-St. Petersburg sounds nice too.
