Safliya island is probably nice at this time of year. The Diplomatic Club will take you there are pick you up later for a reasonable price (especially if you go with friends and split the cost).

The Broadwalk on The Pearl has events going on at the moment (all free). Gotta be worth a trip there just to see what all the fuss is about, even if the entertainment isn't your sort of thing.

Hiring a tennis court at Khalifa Tennis Complex is pretty cheap.

Ice skating.

Join baldrick and his crew on a photographic evening.

Explore outside of Doha; north to Furawit(sp?), north west to the fort, west to Duhkan area.