It seems like it would be a waste to come to Rome and not see the Colosseum. If you're even remotely into history then this is a must. Super busy and touristy in Summer, and very open in parts so ensure you have sun protection. The museum on the upper level has lots of interesting bits and pieces.
Tip to skip the line: buy the Roma Pass from the tourist office up the road. You then get free entry to this and another attraction, then reduced tickets at other participating attractions, plus three days of travel on all public transport.