Just adding to the comments. Museum of Islamic art is a definite ..the architecture and exhibits are great

The national museum is architecturally interesting but the exhibits and info not that interesting.

We loved the national library. Special exhibits and the vault of rare manuscripts. Its a little farther out but also in an intersting area with a lot of university affiliated buildings .meg a cornell medical school

The pearl..not sure what you want to see there

And a contrary opinion on the souq..the market side has been rebuilt and is pretty sterile and new by souq standards.Not terribly interesting. There are restaurants and the like which might be more interesting.

We also thought some of the more moderate malls To be really interesting for people watching since you see the other side of qatar..the workers from Asia and India sending money home from western union, grocery and clothing stores..this is a much larger population than Qataris. We did not use metro..took taxis around.. depending on the time of year..a 15 minute walk can be hot.