Easyjet has cheap flights from Gatwick or Manchester to Sofia. They are even cheap in summer if you book early enough.
Fun things to do in Sofia - hang out at NDK and watch life go by; eat at the vegetarian Sun & Moon cafe or the funky Made in Blue; and don't miss the free city walking tour. The area around Angel Kunchev Street has lots of cute shops, cafes and restaurants.
Take a train or bus to Popovo. The train is fun and travels through some lovely countryside but it can be hot in summer when the air conditioned bus might be a better option.