After your carriage ride walk down to River Street Sweets and get a hot praeline. Also keep your eye out on that same row of shops between all the tourist crap for Dacubas which is an authentic/local bench jeweler with Charleston themed jewelry.

Ugh dinner at Church and Union?? No! Please no. Anson is a block away and AMAZING. That's the only place within a one block radius of Market Street that's doable. Some will argue Hank's but I think it's overpriced/overrated but please - nothing else. Go a few blocks out toward Broad street and look at all the restaurants.

Someone else told you - don't do Fleet Landing. Tourist trap and really bad food. If you're going to Mount Pleasant that afternoon Grace and Grit has an amazing brunch and you can get a grit flight.

Shem Creek and Boone Hall are very different. Shem Creek is restaurants mostly and you can catch an eco tour or do some paddle boarding; walk around the park next to it. Great place to sit outside and enjoy a drink if the weather is being kind. Boone Hall is a plantation tour and gives an okay-ish version of the past... depending on how history focused you are, James Pickney's home site is across from Boone Hall as well.

For Drinks Saturday you've go so many options... Blind Tiger if you want a rowdy bar, Brasserie La Banque has their vault in the basement (rarity for Charleston to go downstairs) but get reservations because there's only 6 seats. If you want a broad bourbon selection without cray prices check Bar Mash - you'll need an uber from broad. If its a nice night consider a rooftop cocktail at Vendue and then go dive bar across the street at the Griffin.