If you get a job in a rehab/LTC facility, don't avoid it just because you're afraid you won't get a job in a hospital. Plenty of nurses make the move from these facilities to hospitals; I've actually known a couple of them that have successfully done so. Plus, these facilities aren't as lacking in skills as one might think. At our facility, we get IVs, PICC lines, tube feedings, bladder scanning, catheters, ostomies, many wounds in addition to the massive amount of medications we pass. The patients aren't necessarily medically stable, either, so you'll have acute situations that happen. Plus, you have many patients with cognitive/memory issues and a LOT of falls.
With that said, if you are offered an acute care position I would consider that just because the workload in rehab/LTC is very, very large. During the day, you might have up to 20 patients, and at night, possibly 56 patients. It can be hard for me to keep up and I've had a couple of years of experience. I imagine it's probably overwhelming for the new grads who start and are expected to take a full load almost right away. When I say right away...pretty much after 5 days of orientation, you're expected to be on your own. In a hospital, you'll get at least a few weeks/months of orientation and your patient load won't be so large.
BUT...if you can't get a hospital job, go ahead and go for rehab/LTC. Whether or not a future employer decides not to hire you is based on personal preference. It is certainly not true that no acute care managers ever hire a nurse with rehab/LTC experience.