Why not go and look now? Standard practice is you turn up unannounced and they show you round there and then. I viewed about 12 homes and all showed me round straight away except two, one was in the middle of a staff meeting and asked me to come back in an hour the other had a policy of not showing people round during meal times, so again come back in an hour.
You don't have to wait for a room to become available before you look round they can put you on a waiting list if there isn't one. We've had a few residents "parked" in the home while they waited for a place nearer their family, a faith based home or just somewhere the family preferred.
If the LA have found him a place then you may have to take that short term at least, you can give an NHS bed to someone who doesn't need it.
After you've visited all 3 you might decide the one the LA have picked is the best so end of problem.
Homes that take LA funding often have a longer waiting period as social services will queue jump if they have an urgent placement ahead of anyone on the waiting list, but that may be how they've managed to get this place for your dad.
Just visit all 3 you could do that in a morning, but if the other 2 don't have places then I think it's best to take the place available at least for now and give the NHS bed to someone who needs it.
K