The town of Hurghada has a small market street for tourists, but otherwise doesn't offer much for visitors to the Red Sea resorts--except for a taste of the way typical Egyptians live. Most of the hotels along the Red Sea are self-contained resorts, ideal for families who don't mind being isolated from authentic Egyptian culture for the duration of their trip. Some resorts connect, so it is possible to visit the shops and restaurants of other resorts if you tire of the same buffet dinners offered by your hotel night after night.
Hurghada can be reached from Cairo in an hour by air for about $230 round trip (Egypt Air). There are also direct charters from Europe in the winter high season. From the airport in Hurghada, you will probably take a shuttle provided by your hotel.
International Fast Ferries  runs fast boats to Sharm el-Sheikh on the Sinai peninsula, currently running four times weekly. The ride takes 1.5 hours and costs 250/450 LE one-way/return for foreigners. Warning: this ride is notoriously bumpy and prone to cancellations.
Your hotel or a travel agency associated with your hotel will be able to arrange excursions to nearby attractions, including Luxor. Luxor is about 4 to 5 hours by bus, and your tour operator will be required to leave and return at designated times in order to travel in a police escorted convoy (of approximately 150 other tour buses.)
Of course, the main reason to visit Hurghada is for the beautiful Red Sea, which is excellent for diving or snorkeling. If you aren't licenced to dive, it is often possible to snorkel and see incredible coral reefs and hundreds of varieties of tropical fish just 10 meters from the beach. Again, either your hotel will have dive escorts on site, or they can arrange a scuba diving expedition with guides. In late March, the water is still quite cold (21 Celsius), so a wet suit is necessary, and even snorkeling in a bathing suit is too cold after about 10 minutes. It is also windy in late March; sustained 20 MPH are common. Make sure your Beach resort Hotel provides wind screens on the Beach.