While the bk is really going to hurt you, especially with Chase and Citi, two of the big ones, this summer is going to be hard to get enough points by, depending on where you want to go, how long you want to stay, and what you want to cover with points. I have 8 cards in my churn I'm working on right now, the latest closing one has a spending requirement date of August, and if points don't post for 4-6 weeks as some don't, it will be October before I see them.
I'm definitely going to re-iterate, work on getting your credit up, most of us have high 700s, with no bk.