this might just be pure ignorance on my part, but what is a great ortho hospital without a residency program? Unless it's a hospital that residents routinely rotate at and is part of the residents experience?
I would personally not do one there. At a rotation with residency programs you can get all the things you want (good letters, etc) AND most importantly, exposure to a residency program both for your sake (to see what this program that you could be interested is like and if you like it) and for their sake (to see if you are a strong candidate and would work well within their system, exposre to residents, who are really the ones that determine if you'll be getting a good LOR from a given rotation).
I really don't see any added value in rotating at a non-ortho residency program....but i'm just a 4th year in the process of applying, so take my thoughts for what they're worth.