> should we plan on picking up the car at the airport
> or wait until we are ready to leave Philadelphia
> and rent one in the city near our hotel

You will NOT need a car for the two days you are visiting Philly. The cost of renting a car at the airport, however, may be so much less than the cost of doing so downtown, that it MIGHT be better to rent the car at the former. Or it might not -- there are just WAY too many variables. You'll simply have to do the calculations on your own. As you calculate the cost difference, don't forget to factor in the cost of parking the car for two days near your hotel.

> where to stay that is near museums

Philly is sufficiently compact and has such a good mass transit system that you can stay just about anywhere in Center City and easily get to all museums and historic sites by foot, bus, and cab. Pick a place that meets your budget and has the amenities you want, and then find out how to get to where you want to go.
Note that I said "Center City." There are hotels on City Line near the Schuylkill Freeway that are perfectly fine places to stay, but are inconvenient to anything you'd want to see.

> and is safe!

There are parts of Philly where I would NOT recommend driving through in daylight, let alone walking through at night. Fortunately, and not surprisingly, none of these areas have hotels or attractions for tourists. To be 100% precise, here's an official map of crime in Philly:
https://www.crimereports.com/agency/philadelphia

we were there last july (with twin 1 year old boys so we needed convenience more than anything). You don't need a car in the city and as a matter of fact, it will just cost you parking which isn't going to be cheap. We stayed right in downtown and you can take the subway to the 30th street station. Alternatively (and this is what we ended up doing since the price turned up the same but we were doing one way drop off in boston anyway so do shop around and see what the best deal is that you can come up with), was rent a car at the 30th street station. I agree you shouldn't rent in the other city locations but the 30th street one was comparable for our needs.

On the day you leave, go to 30th street station from the city via the subway system, then connect to PHL airport to pick up your car (should only be a few dollars for the tickets). Once you have your car, call your family and tell them to get your belongings down to the lobby and check out. Pick them up at the curb. Easy peasy.

Not sure when you are going or what you enjoy, but a car would allow you to visit Longwood Gardens and the wineries in the Brandywine River Valley.

With only two days, there is so very much to do in Philadelphia that a car would just be an unnecessary expense, both the renting and the parking.

If you like art, do of course get reservations for the Barnes; also along the Parkway is the small but lovely Rodin museum. Non-art museums that I really enjoy include the U of Pa Museum of Archaeology and Anthropology, the new National Museum of American Jewish History, the rather eclectic and Chihuly-laden Liberty Museum, and of course the small but stocked Philadelphia History Museum at the Atwater Kent.

If you're more into the colonial history, the Holiday Inn at 4th and Arch is a great location for exploring Old City and Colonial Philadelphia. Otherwise, just about any Center City spot is fine. As PaulRabe says, the transit system makes it easy to get around and the most visited parts of the city are quite compact. (Walking is my favorite method of transportation!) There actually aren't too many places I wouldn't ride through in daylight, but I agree that it wouldn't be a great idea for visitors to the city to wander alone at night in some of the outlying neighborhoods. But that applies to pretty much any city.

visitphilly.com is the official tourist site for Philadelphia. The site has a link for hotel deals.. generally for 2 nights and some will offer free parking.

I would recommend staying in the Historic district or Rittenhouse Square or the Museum district.
I have stayed in the Sheraton Society Hill, in the historic district and I could walk to most attractions; I have also stayed at Penn's Landing which is too far out of the center IMO; and in the museum area. There are buses that go along the Ben Franklin Parkway, a multi lane street where many museums are located.

Even if your hotel offers free parking, you may not want a car as you will be paying for it but not using it in the city. There is really no reason to drive around and parking is expensive

You can easily take the train from the airport to 30th St Station, and then take a taxi to your hotel or the subway if its convenient.

Thank you for all the great info!! We plan to fly into PHL and out of Charlotte so the info about the one way rental was great. Also appreciate the crime info (we are from Oregon and tend to hear all the worst!). Trip is planned in early October. So, no car, and hope to stay in the museum area! Amy- thanks for all the museum info. Not into archeology or natural history, but will be researching your amazing list! Again, thank you all!