Hey there! I spent six months last year living in Vallabrix, a little village right outside of Uzes, as an exchange trip.
You've GOT to visit the Pont du Gard. It's an old Roman aqueduct and it's the main tourist attraction around Uzes. There's a river there which makes for good swimming.
In Uzes, there are many different restaurants and cafes you can visit. During the daytime, visit the Place aux Herbes. The outdoor cafes/restaurants are great to grab some lunch at there. I like la Nougatine for some hot chocolate and croissants; they're located right on the main drag. They're one of the more pricey places in town, but oh my... so worth it! :) This would be a good place to splurge on some birthday cake. Even better, consider sampling a variety of French desserts. My favourite is "charlotte aux fraises" (French version of strawberry shortcake).
There's a food market every Wednesday morning in Uzes, as well as every Saturday morning (they shut the main street down on Saturday. Not only are there food vendors, but clothing and book vendors as well. A must for any shopaholic!). You should check it out, as it is a great place to experience arguably one of the best markets in Southern France. Also, you can find some of the best souvenirs there. Be sure to grab some local pottery, honey, olive oil, lavendar, and herbes de Provence! You could treat your sister to something here :) The chunky bracelets with big beads and dangly charms were very popular with the French girls my age (I'm 17 too) in Uzes.
Consider taking a side trip to St. Quentin la Poterie. It's a charming little village filled with pottery artists that are happy to show you their wares.
The Vallee de l'Eure is the park right in Uzes. It's absolutely lovely. Very typical of the South of France! There's a nice river flowing through it. It's so beautiful in the summer :) Consider taking a picnic lunch.
As for nightlife, well, I can't speak too much about that. I didn't party too much in Uzes. If you and your sister want to go party, I'd suggest looking into bussing from Uzes to Nimes (it's about six euro for a youth one way). Nimes has one of the best preserved coliseums from the Roman times, and now they hold bullfighting and concerts there. Nimes is a great place to party; literally the whole town shuts down and the main street becomes like an outdoor club during some festivals! http://www.festivaldenimes.com/ <= check it out for more info. The legal age for buying drinks in France is 18; some places are more strict than others on this. It's always good to try :)
Hope this is helpful, feel free to contact me with any other questions! :)