I would definitely go solo, solo travel is the funnest because you're not bound to someone else's agenda and don't have disagreements over what to do and where to go.

I also think that getting away from your current 'environment' will help you adjust to the breakup and clear up your mind.

Definitely, go and have as much fun as you can, not allowing bad thoughts about the breakup to creep in by simply ignoring them or letting them pass by. The best advice I've ever received about negative thoughts is that they are just thoughts and you don't have to believe them.