Scooter recommendations for FIL?

Motorized wheelchair is the way to go as they can turn 360 without needing a large space. Scooters require going forward and backwards and forward snd backwards constsntly turning the steering to be sblevto turn around in tighter spaces ..especislly in elevators which require being able to drive in reverse! We bought moms on craigslist. Local Ebay. Check other sites like nextdoor app. Where u can post a iso. Not worth buying new. We also bought the replacement battery on Ebay

There is a possibility that if you can get the doctor to agree, and given the conditions. The fact that he can barely walk with the walker and he is not strong enough to use a wheelchair that a motorized one might be covered.
It would be worth checking that out.
A PT should assess it and his need for the motorized scooter.
I would also try several types before settling on one.
You might also find a used one on line.

Remember the days of scooter commercials on TV? Every five minutes?

Well, the seniors back then took advantage of those ads. So much so that Medicare was dishing out tons of money for scooters. It was one of Medicare’s top expenses. Now you have to jump through hoops for a scooter.

Try Craig’s list or Marketplace. First check with the facilty if they are allowed.

We found one at a garage sale by the family of someone who had just passed.  I don't remember what we paid for it, but it was in good condition and worked quite well.

It was battery operated, so it had to be plugged in periodically for charging. 

Dad didn't need it for rehab, was never in AL, but I do recall that at least 3 of the rehabs he was in had space for scooters.   I do recall seeing a few residents using them, sometimes with assistance from an aide or someone else. 

Besides providing transit, I thought that one of the important aspects was to convey a sense of self reliance and freedom.

My dad was wheelchair bound and wanted to use his motorized scooter but PT assessed him for safety and said he would trip or fall and be injured using it. So he really should be assessed first.

I agree that a power chair is a better option! A scooter is too dangerous! If you are insured, you will need to be referred by your doctor or PT. If you have to pay out-of-pocket, a power chair is quite pricey!

If he is in assisted care, why isn't he being assisted to dining room, etc.?

I don't know if he is or is not mentally and physically capable of handling an electric wheelchair. That needs to be determined. If he can handle it, the doctor can provide an RX for an electric wheelchair and Medicare will pay for it - no cost to you. And if not, the aides at the facility must push him to the dining room in the wheelchair. I live in assisted living and the aides push the wheelchairs.

The dining rooms I've seen tend to be crowded and all the walkers etc need to be left out in the hall, unless he is able to park and continue on to the table unassisted the scooter might not solve the problem. I like Grandma1954's advice about a motorized wheelchair, he would be able to take that right up to the table.
It might also be time to consider whether the AL is going to work for him long term, if getting oneself to the dining room is mandatory what happens when he loses that ability even with the aid of a power chair?

Have you asked the AL about a scooter? Maybe they have some ideas. It would need to be something light and portable. That he can drive with no problem.