we are staying for 2 nights at the two Meeting Street Inn. Do I need a car? What are the interesting places to explore? Are there good restaurants close by? Any suggestions would be appreciated.

You shouldn’t need a car to explore things, for the most part unless you want to visit outlying plantations and such.

What kind of food do you like, and what kinds of attractions interest you?

Have you searched for any threads here to help you narrow it down.

"Are there good restaurants close by? "
Charleston is heaven for foodies!
I particularly like Magnolia's.

"Are there good restaurants close by?"

Yes.

Telling us exactly why you chose Charleston in the first place would be the best suggestion. Great city and experience but since we have no idea why you are even there we cannot help much. Who knows? You might actually like Savannah better.

Charleston is a hot bed of good eats. Magnolia is a bit old school, but is a great place. I also like Hominy Grill for lunch. If you plan to stay in Charleston proper, you should be able to Uber/Lyft for any excursion you take.

For the most part, you don't need a car in the area of Charleston you are staying in. If you want to go out to the islands, you might like a car but 2 days - no car needed. Charleston historic area is quite walkable.

Tons of restaurant choices:
HUSK, Magnolias, Slightly North of Broad, Peninsula Grill, Hall's Chop House are great dinner choices. Husk's bar is also terrific and there are tons more up and down King Street. Callie's Hot Biscuit in the Charleston Market and also on King St is a great little breakfast option. The bar at Charleston Place is also lovely. We also enjoyed Tavern and Table on Shem Creek.

If you are there for only 2 days you would do well to plan it very well in order to enjoy it to the max. Restaurants are certainly one of the primary enjoyments. Decide and make reservations. You are staying at one of the prime properties so that is a plus. You won't see everything but can get such a taste you can't wait to return. Do NOT spend much time at the Market--it's a tourist haven. Do quality--of course, the historic part of the market being there is prime.

There are a number of trip reports on Charleston. If you click on my user name, you will find my trip report. If you query this forum, you will find all of the answers to your questions.