Any places able to visit in Luberon without a car?

Your best bet for Luberon villages would be a tour from Avignon. Buses reach Apt from Avignon, but you'd need some local transportation to get around to the villages (e-biking could work but not for beginners as the roads aren't traffic-free).

On the edge of Luberon, l'Isle sur La Sorgue is accessible by train from Avignon and bus from Aix, and is worth considering for a day or two. It is more of a small town than a village, but it is quite charming, with a great antiques market on Sundays.

Thank you. Is Apt itself worth visiting/staying?

It is a very typical Provence town. Not the cutest, but still very charming. Especially worth it if your stay coincides with the Saturday market.

I checked again and buses from Apt are better than they used to be, with several daily buses to Gordes, Bonnieux, and perhaps some other villages.

Also, I am sure that you can easily arrange tours from there, or even taxis to nearby villages. You will not have the same access to group tours as from Avignon, but proximity will help keep costs down.

Bike tours might be available: Apt to Roussillon is a mere 7 miles, Goult is 10 miles, Ménerbes is a bit further but mostly flat. A bike trail along a disused railway on the main D900 helps for pleasant outings - but all villages are on hills on either side of the valley that the trails runs thru, and traffic, while light, can be fast on the country roads.

Last but not least, hiking to pretty Saignon is feasible, it takes about 1:15 hour one way. Or you could take a cab up, and hike down (900 ft elevation difference).

I do not have firsthand info, but perhaps the local tourist office could be of assistance.