Easyjet has cheap flights from Gatwick or Manchester to Sofia.  They are even cheap in summer if you book early enough.

Wizzair flies Luton to Sofia.  British Airways flies Heathrow to Sofia.

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.