We are planning to travel to Provence July for 2 nights with a car. Should we skip this area due to the Avignon Festival? I am worried it is going to be crowded and not enjoyable in the overall Provence region. We do not plan to stay in Avignon but would like to see the city.
No reason to skip the area: only Avignon will be crowded. You can still visit - it's a fun crowd - but with only two nights Avignon would not make it to the top of my list. Arles, les Baux, Luberon villages are more charming to me.
By the way, where are you planning to stay?
If you haven't already booked lodging, I'd suggest doing some checking on a website like booking.com to see what's available for your dates in places you might like to stay. In 2017 I found that a special event in Arles affected availability and drove up rates in Avignon. I'm guessing the reverse could also happen. There's good rail service between the two cities, making it not terribly incovenient to day trip between them.
Two nights is a very, very short stay in that area, though having a car at your disposal will help. If I were wedded to the idea of including two nights in Provence on my itinerary, I'd be inclined to take advantage of having the car and go to a bunch of the smaller towns and villages. It's very easy to see Arles and Avignon by train, and even St-Remy is manageable from either of those because it has bus service, so I'd leave places like that for a later trip when I had more time.
I will caution you that going to L'Isle-sur-la-Sorgue on one of its market days (Thursday and Sunday) would probably use up a lot of your very limited time. It's fun, but it's a zoo, and I assume traffic and parking are both challenges.
We haven't booked where to stay yet. We are trying to get the itinerary straight first. Open to any recommendations. We are going to Paris, Loire Valley, Chamonix, and Nice (Saint-Paul-de-Vence) as well. We will splurge in 2 of these places - was thinking Provence and Nice.. I found Hotel Crillon La Brave for potential in Provence as a splurge hotel. Open to suggestions. This is our first trip to France. It will be my husband and I as well as our two early 20's children.
Hotel Crillon Le Brave is an amazing splurge, never stayed there myself but visited family who did, so I saw the grounds. There, you would be far, far removed from the crowds of Avignon and perfectly positioned to visit the wine country to the west (Gigondas, Séguret...), Vaison to the north, lavender country around Sault to the east, Luberon villages to the south. Two nights is tight so you will have to make choices, but whatever choices you make will be good ones, and you will come nowhere near the crowds of Avignon.
What I do not recommend is going up Mont Ventoux. In a way, it is too high up above the surrounding areas, so the views are often hazy.
If you are hesitating re. the price tag, my parents stayed at La Maison de Crillon in the same village 2 summers ago and absolutely loved it. It's still very high end, but closer to €400/night than the €600-800 charged by the Hotel.
How many nights do you have in mind for your other stops, by the way?