I really can't answer your question with a recommendation for a specific hotel, but I can share the process I would use if I were in your shoes.
I would go to a site like hotels.com to compare hotel prices for my specific night. Then from the hotels in my price range I would go to the hotel website or even call the individual hotels to find out their policy about how long you can park free on a park n fly stay. I would guess hotels have different policies.
If it ends up you can't park free anywhere for that long I suggest you park at Economy airport parking. I believe their $5 nightly rate is as cheap as you will find and they have good service.
Hope this was a little helpful.