Charleston is a waterfront town with a beautiful harbor and a gorgeous street, Broad Street, in the French Quarter. In Charleston, you find a real mix of complete dilapidation (most of the city) and a few attractive spots. Many of the buildings in Charleston are boarded up, have balconies falling off, and are covered in grime. The architecture is very dense, with tall houses built on top of each other, with balconies facing the next house just a few feet away. It can be a little discouraging to see when you've heard so much about how beautiful Charleston is. To see the beautiful parts, you have to really know where they are: the French Quarter around Broad Street. There are plenty of hip spots as well, in industrial areas, such as The Daily on upper King Street, and they are fun to visit too.

For a truly beautiful street head to Broad Street in the French Quarter. At the end of the street is the gorgeous Old Exchange and Provost Dungeon building. I found it a bit too musty and the tour too slow, but it's lovely to walk by it, on Broad Street. Palms stretch up to the blue sky, while ornate colorful storefronts delight your eyes. Pop into Washington Square and admire the incredible oak trees that twist with all that Southern charm. There are statues and fancy benches galore. Chalmers Street, on the north side of Washington Square, is a cobblestone street with gas lanterns. If you head a block north you will come to Gibbes Museum of Art, which is a lovely art museum you will want to spend an hour or two savoring. Make sure to enjoy their coffee shop, The Daily, that also has soups, salads, and sandwiches. It has the prettiest decor and is so relaxing to sit in.
Check out St. Michael's Church, the pristine white church with the tall steeple, and a pretty graveyard. Across the street is City Hall with its curved staircases. The Postal Service building is amazing with its chunky sandstone bricks and castle-like shape. There is a Postal Museum inside.
Head down Meeting Street, peeking through fences at tidy gardens. What gorgeous buildings everywhere! There are just layers and layers of beauty to feast your eyes on! Notice how grand the columns are in front of the buildings even if they are not very large buildings. 
Walk to Waterfront Park to find a wonderful promenade on the blue water! Look past the adorable salt marshes toward the harbor. You can see the USS Yorktown and the Arthur Ravenel Jr. Bridge, a marvelous bridge. In Waterfront Park, check out the Pineapple Fountain, a unique creation. Everything is pretty here!
Next to the park, dive into Belgian Gelato and try their poffertjes, little round Dutch pancakes. 
There is a pub and some nice-looking cafes on Broad Street or you can walk up King Street to find popular stores like Forever 21 plus more cafes. This area is a mix of highend stores and really rundown spots, and not as pretty as Broad Street. Street parking is a hassle here, as it is in most of the town, and very expensive in the lots. The museums and attractions in Charleston all run very high in admission price. You will see many dilapidated buildings as you walk up King Street and around its side streets, and places that seem like they would be nice, like Marion Square, are not. There are many homeless people in this area.
For a hip scene, drive to The Daily (on the far north end of King Street), a coffee shop and counter service cafe in an industrial area. It is popular with a steady stream of young people. Sit by the big windows on picnic table style seating. They have delicious teas, amazing chocolate croissants, good chocolate chip cookies, unusual meals, and cool music. This is a handy place to eat because there is a parking lot.
If you're tired of the city grunge, drive over the Ashley River to James Island and eat at Charleston Crab House. It has great atmosphere and is on the water, at Wappoo Creek. The prices are high but you can get a mahi sandwich for $15. The grits are out of this world yummy, as are the lima beans, so choose them as your side!  
While in Charleston, visit a plantation (many are west of town at Ashley River Road), one of the nicest things you'll do during your stay. Magnolia Plantation has lovely gardens full of flowers, and incredible twisted oak trees covered in Spanish moss and resurrection ferns. If you take the Nature Tram tour you can see alligators, which we did! Another place to see wonderful Southern-style oak trees is Charles Towne Landing State Historic Site, which is less expensive than Magnolia Plantation. 
Don't miss the other side of town, east across the Arthur Ravenel Jr. Bridge. It is lovely! If you park at Mt. Pleasant Pier, you can see the bridge from a little side pier with swinging porch chairs. There is an amazing playground that looks like the bridge, and is in the shade of the bridge, perfect on hot summer days, too cold and windy on winter days. Here people play frisbee on the huge lawn. You can pick up a picnic at nearby Whole Foods or Trader Joe's to have on the lawn.
Also across the Ravenel Bridge is Patriot Point, a fascinating place to visit with amazing views! Try to come on a sunny day to really enjoy the bright colors all around you. The blue sky, blue harbor, green marsh grasses rising out of the water, white bridge, colorful harbor buildings. Lovely! The USS Yorktown airplane carrier warship is here, as well as a powerful Vietnam Experience exhibit. From here you can catch a boat to Fort Sumter for a two hour excursion. 
Nearby in Mt. Pleasant, eat at Saltwater Cowboys, which has perfect views over the water. It is a true delight! Go to the top for panoramic views at sunset, or to the bottom level for a bar with cute lights and a fire pit. Or stay on the second level for wonderful views out their sweet windows. The food is just ok.
Continue on to visit Sullivan's Island, and either Sullivan's Island Beach (which is more exposed) or Isle of Palms Beach, which has a cute main strip, Ocean Blvd, where you can get a Ben and Jerry's Ice Cream in an adorable tiny red-roofed building. Between Sullivan's Island Beach and Isle of Palms, stop at Thompson Park to see the picturesque views of Breach Inlet and read the interesting history plaques. Also on Sullivan's Island is Fort Moultrie, a fascinating place to visit and easier to see than Fort Sumter.
While in Charleston, you can also visit the South Carolina Aquarium, a short drive from the King Street area. It is an attractive aquarium, nicely done, in a large two-story waterfront building with river otters, tropical fish, sharks, pretty views...but with a hefty admission fee.
In the King Street area, if you have kids you can visit the Children's Museum of the Lowcountry, an imaginative and wonderful place. Kids will adore playing in the medieval and pirate areas.

Directions

The pretty area of Charleston is around 122 E Bay St, Charleston, SC 29401. From here you can walk along Broad Street (the French Quarter) and the surrounding streets and also walk to Waterfront Park and the Pineapple Fountain.

Click on map for interactive view