Questions prior to my upcoming trip to Lisbon/Sintra

Sintra is super easy and cheap by train, I can not imagine any reason to rent a car for that.

we are planning on booking an excursion (convertible jeep that off roads) that covers the hottest sites in Sintra

I'm struggling to understand this. "Hottest sites in Sintra"? ???

Thanks David! The consensus seems to be no car from folks, so good to know! As for the, "hottest sites"::
1. Pena Palace and Park
2. Moorish Castle
3. Palacio Nacinal de Sintra
4. Quinta da Regaleira and Gardens
5.Old Town
6.Palacio de Monderrate
7. Convento dos Capuchos
8. Santuario de Peninha
9. Sintra-Cascais National Park
10.Adraga Beach and Cabo de Roca cliff (the westernmost point in mainland Europe)

I've been doing a lot of research. Some close some farther out I believe.

I had a car when visiting Sintra (stayed in Sintra but on the coastal part not the old town) ; anyway with a regular rental car I could drive to each of the sites you mention, there really was no where an off road jeep could have taken me I was not able to myself

There is a beach close to the lighthouse where the dirt road is beat up, so in a normal car it is better to park on the road to the lighthouse and walk the dirt road ; but we are talking a 1/2 mile at most dirt road in one spot and the Jeep would not help what is a difficult steep climbing trail down and then back up from the beach.
Your list of 10 did not include this place though.
I don't recall seeing any other dirt roads and no where looked off road able.

The list of 10 sites you mentioned is definitely more than 1 can see in 1 day.
9.) This is actually the entire region, it is not a National Park like we think of ; all of Sintra from the old town to the coast and each inch between is considered the park.

Hi twigglebop1! Can't help you with baggage question. If you are traveling from the US, by the time you get through immigration and customs, then get into Lisbon, it will likely be 1 pm or later, not sure it is worth seeking bag storage. If you can, go for lunch or whatever with your baggage. Or maybe have lunch at the airport.
Sintra is terrific, I also spent 2 nights. No need for a car really, I don't think. Highlights of Sintra for me were (a) Palacio da Pena -- I went first thing, and almost no one was there at that time, when leaving the palace itself, I took a very inexpensive tour by extended golf cart type vehicle, through the grounds, gardens and interesting out-buildings of the estate; turns out I was the only one on the tour, so the young driver/guide and I had a lot of enjoyable flexible time and extra stops; well worth the time; (b) Quinta da Regaleira, a very interesting property well worth 3-4 hours; (c) the town itself, with interesting shops and bakeries, street art nearby, etc. I recommend the restaurant Incomum for a great dinner. The Castle is really just a long old rock wall, with views of the town, no longer really a castle.

Your list is kind of a mix of in town and out of town locations
1-5 are in town and car is not needed.

The other 4 (I am excluding #9 since it is not a single location) I am not sure is on the normal public transit route. One or two of them might be and a couple are definitely drive yourself or get a private driver to go see which will make them considerably costly so better be high on your priority list.
I really like the coastal area (hence we stayed multiple nights there) but most visitors going to see the highlights of Sintra for a 2 night stay don't leave the old town area and those sites.

Overall though better first to iron out how long you are staying and where in Sintra. After that make your list of what you want to see. The 10 you currently listed are a more to do then you time allows.

Thanks to all for the helpful suggestions! We will be in Sintra for 2 nights and three days. Luckily, the bulk of those sites I listed, are included in our convertible Jeep excursion. I like the idea of using the first day to explore the old town and dine at a nearby restaurant. I am definitely leaning toward no rental car.

Thanks again everyone! I'm sure I'll have more questions before I leave on 11/21!

Think you will have a great time in Sintra!
Just cautioning you that the convertible Jeep tour may sound a little nicer than it is actually is.

Not sure the time of year will be ideal for top down weather enjoyment.
There really is no off-road component.
Any vehicle gets stuck in the same awful traffic around the old town and on the one way loop to the Pena Palace area.
In Sintra (at least for the Pena Palace) you do much more waiting in line, inside a vehicle, on other lines, etc...
The Jeep cannot drive through the gates to the Park so is only serving the purpose of getting you from one line to the next.
In the case of the Pena Palace and it's large surrounding park ; that area is all gated off to any vehicles except for their own bus that goes up to the castle for an extra charge and always has lines as well. The Moorish Castle wall area is practically across the street so no need for a vehicle to go from one to the next and because of the one way loop you actually would need to visit the Moorish Castle first if on a vehicle tour that does not park. The Moorish Castle likewise has a gate where no vehicles can drive past and then you need to walk down a path from that point to reach the actual site.
Due to lines and walking required each site takes a good amount of time to visit.

Not trying to talk you out of it, if it offers you a way to see the coast and some of the other historic sites that are in between town and the coast and hard to reach than the tour may be your best option.
If you are utilizing the Jeep tour to reach the out of town sites all in 1 day and then on another day visiting the in town sites on your own ; then that would make sense.

Don’t use luggage storage at the airport as it’s too far to go back out there. There is luggage storage at Cais do Sodré - which is the train station with the train to Belem. There are a lot of restaurants and the time out market close by for lunch.
You really don’t want to drive in Sintra. They have made a lot of streets one way in the last year, making traffic worse than ever.
And, I’m one that hates the public transport in Sintra so your jeep tour sounds like a good option.

I've always been able to arrange to drop my luggage off early at my Airbnb, often to check in, too. I'd try that first. It's not a long trip to the airport to pick it up, but it would take considerable time to get there, get the luggage, and get back. It would definitely be better than the people I saw dragging their roller bags around the cobblestones of the Castello for a couple of hours, though!