Montauk is awesome in the off season but I’d say it’s a bit far for a day trip. It’s like 3 hours each way on the train. If you can stay overnight, probably a better use of time. You can find cheap hotels/motel this time of year (at least you could pre COVID-not sure if it has changed!)

I travel solo a lot. For shorter trips, I prefer hotels-if it’s an early checkout or you get there early, you can leave your stuff at the front desk, use that bathroom. Get advice from the concierge. Also hotels generally have way more flexible cancelation policies. I prefer Airbnb when I am doing a longer term stay. Usually the rates go way down, and I’ll message the owner directly to negotiate. During the pandemic I rented a whole beach house off season for 6 weeks and it was way cheaper than a hotel would have been. Also-once you establish a good relationship with a host, you can usually deal with them directly and leave Airbnb out.