Charleston, SC

I don't know where you have reserved in Savannah, but a few years back we stayed at Planter's Inn on Reynold Square in Savannah. It was great! and the prices were pretty reasonable. You might check it out.
Just fyi, in Charleston, if you want to visit a plantation, I recommend Boone Hall for a more realistic picture of plantation life, and especially the Gullah culture. It isn't just about a fancy house with pretty furniture. It is in Mt. Pleasant. I am sure you can get an Uber or Lyft there from wherever you stay. I don't have any recs for hotels in Charleston. When there, be sure to visit the Old Slave Mart Museum. There are recordings made during the 30's of survivors from the days of slavery. And take a carriage ride around the old city. There are ones with different focuses.
Have a great time!

The Charleston Festival is on certain weekends in March & April. Plan accordingly...It's on my "to experience" list, but if you aren't attending then you wouldn't want to necessarily be in Charleston then.

We visited Savannah & Charleston last March and loved both, although I liked Savannah more. I did find Charleston to be much more expensive. Our hotel in Charleston was $100 per night more than our equally well located hotel in Savannah, but in no way could hold a candle to the Savannah accommodations. If you stay in the historic district of Charleston, I would recommend a hotel with a restaurant (at least for breakfast). We had rain one day and the whole area flooded. We could not leave the hotel until the water receded, which meant nothing to eat until after 2:00pm which left me a little cranky. I cannot recommend our hotel as I would not stay there again.

Also doing some planning for Charleston and Savannah during an upcoming April trip! Found Charleston to have really inflated hotel rates compared to Savannah. I’m told the dining scene is similarly skewed expensive in Charleston.

Mt. Pleasant will make a great option to Charleston. It’s only a 20-minute ride on bus #40 to Charleston’s Meeting Street or a 10-minute Uber ride over the bridge.

Note that Savannah is largely historically intact with much of its period architecture whereas Charleston’s original buildings were mostly destroyed during the Civil War. First, there was a devastating fire in 1861 that leveled most of Charleston. Then, as Confederate soldiers retreated from the city in 1865, they either blew up or set fire to most of what remained of Charleston. When Union General William T. Sherman entered the city, he reported that Confederate forces had done his job for him —leaving little standing in the city where the war began.

I grew up in Mount Pleasant! I would definitely recommend staying there. It's close enough to easily get downtown and also has good restaurant options, which are likely cheaper than downtown Charleston. Patriots Point and Shem Creek are two areas in close proximity to the bridge. If you stay in Mount Pleasant, you're also close to the Isle of Palms and Sullivan's Island, if going to the beach is something you're interested in doing.

Sounds good. Not that you are suggesting it, but the one thing I would say is avoid North Charleston. It’s near the airport and has some decent chain hotels which will offer attractive rates, but the area is run down and dangerous. I’ve stayed there as I had business there, which is the only reason to do so.

Both cities are wonderful. Charleston is more expensive, but there is lots to do there.
Consider going on a boat tour to Ft. Sumter.

If you have more time, you could add the Golden Isles, which are near Brunswick, GA. St. Simons island and Jekyll Island are worth a visit, also, continue down to Florida to see St. Augustine.
Jekyll Island is interesting, it was once owned by a collection of millionaires that built "cottages" and had a hotel built in the 19th and early 20th Century. There is a great Turtle center where injured turtles are in a sort of hospital for recovery.

Historic Charleston Foundation will be having their annual Home and Garden tours from March 18 to April 11 this year.

HCF Home & Garden Tours
The tours are at your own pace. You get a wrist band and map of the tour area. There are docents at each location.

Up the coast in Georgetown, the parish of Prince George Winyah has plantation tours each spring. This year the dates are March 27-28. You will need a car for this. Prince George Winyah Plantation Tours

Also, since you will be there in the spring, you might like the plantations along the Ashley River >> Drayton Hall, Magnolia and Middleton Place. Magnolia Gardens will be in full bloom. There used to be a discount if you bought tickets for both Magnolia and Drayton. They were owned by father and son. Drayton has a pre-tour talk about the people of Drayton which is very interesting. Drayton Hall house tours are timed and led by a docent.

I would suggest paying more and being in Charleston if your budget permits. There is nothing wrong with Mt Pleasant, but it’s not Charleston. Traffic is an issue and commuting may be more costly than the hotel price difference. If you are leaning to MP, Use Waze or another app to look check how far and how long it will take to get into Charleston.

I grew up in the Charleston area, so just strongly echoing the previous recommendation:

If you are leaning to MP, Use Waze or another app to look check how
far and how long it will take to get into Charleston.

I would rather pay one transport charge from the train station and walk all over downtown Charleston versus paying taxi fares every day. I don’t know anyone who has even taken the bus, glad to be wrong on my pessimism about that though. I can 100% attest to traffic being an issue.
Without a car, you will miss a lot of the really unique things about the area, but with just a day, it makes sense to focus on downtown. To my great consternation, and one of the reason I don’t live there still, this is not an area that values public transport.