You can decide when you want to sue them, and can sue them for damages accrued through the date you get what will presumably be a default judgment against them. If you want to wait to sue until you find a new tenant, you can do that. I don't expect that this person will be paying off any judgment you obtain, so you probably don't want to put yourself in the position of suing more than once (for damages through date X then again for damages from the next day through the end of the lease or the date you get a new tenant).