In the Rhode Island tradition, I'll try and explain what's available now vs what used to be. Please note that things may change further by December.
1) Rhode Island Airport Corporation owned parking (operated by LAZ) - Garage A is the closest, followed by Garage B (coupon rate available via the parking links on the pvdairport website). There are 2 uncovered parking lots -- Lot D (walk to terminal, used to be considered short-term parking) and Lot E (shuttles to terminal, used to be considered the long-term economy lot). As (presumably) a cost-savings measure with declined air passenger traffic, Lot E is currently closed and the smaller Lot D is accepting the economy lot discount coupon available on the website.
2) Red Beam Garage Garage C (used to be RIAC owned) - is just after Garage B (they're all connected; you're just walking through them to get to the terminal). They have some sort of reservation and discount available on their website.
3) PreFlight Parking - no longer in operation (also Legal Seafoods left that space to open a location nearby in Cranston; the former Legal space is now occupied by an Italian restaurant, Tavolo)
4) The Sheraton referenced above changed branding and became a Wyndham. For a while it was closed to regular guests and used as COVID-quarantine housing for vulnerable populations. However, I don't know if it's still being used as such since I no longer see the National Guard or law enforcement vehicles stationed outside it.
5) There are a number of hotels/motels in the area that offer park-stay-fly packages, however I'm not certain what's actually open. For "walkability" to the terminal, there's a Fairfield Inn adjacent to those parking garages (I think you can walk through Garage A to get from that hotel to the terminal). There's also a Hyatt Place that's on Jefferson Blvd. next to the rental car garage (connected to the terminal by a skybridge to safely cross the extremely busy Post Rd.; it's a loooooooong walk, but there are several speed ramps to help. In the past they would have an electric cart driver going back and forth to assist passengers, but I haven't been since COVID so I don't know if that's still available).