You want a competitive rate — no closing costs. Your bank should tell you right away what your rate would be on a 15 year mortgage for that amount — IF you give them your credit score, the value of your home, and the amount you want to refi. They will try to drag you through the process — but just ask them to be specific on the current rate.
And yes, try Rocket Mortgage or GuaranteedRate.com. They are very efficient — at a time when most lenders are swamped with refis. So you want to be LOCKED in to that promised rate at the time of your application.
My source for mortgage info is Leslie Struthers at GuaranteedRate.com (Leslie@rate.com). You don’t have to use my name — I get nothing out of this. And I know her team is swamped, too, because it took her a few days to return my call last week! But she is good!