DiY is the way to go. Drive along the corniche to see the skyline and the Islamic museum of art designed by IMPei ..musuem and the national musuem close at 7 so you probably wouldn't make it. We ate at a good middle eastern restaurant right behind the hilton doha on the beach ..I dont recall the name but great grill and appetizers with large portions etc. You could have a table on the beach. I know some might suggest the pearl but really it's pretty sterile and not that interesting to see.