Varna is very nice place to stay for a while from which you can visit different spots. It is also a very well-preserved city with houses from the Ottoman Empire and begining of 20th century with a very mild atmosphere, and an exceptional sea garden.
There is also a lovely fruit market by the cathedral, where you find fruits and vegetables that you haven't eaten since you left the orchard of your mummy - ripe fruits that smell so good; berries of all kinds, peaches, nectarines, and melons; fresh almonds and walnuts cost almost nothing - you have just to peel them!
Depending on what time of the year you choose to visit Varna you have variety of activities. During the summer time a walk in down town Varna can be very rewarding. For the Bulgarian people having a cup of coffee outside overlooking the walking trafic (see and be seen) is a way of living. There is a walking passage called King Boris, where the best shopping and cafes are located still. Soon though the shopping scene will change since 2 large malls are in the making and one has already been completed. They are located away from the city centre, closer to the airport. Just a bit off the main street there are multiple little bars, candy shops where one can sit down and indulge in cakes and pastry items, which in western countries would be fit for gourment stores. For the younger crowd there are places with alternative music and interior like "Cargo", "Bola", "La Playa", "A Lounge" Right on the walking strip, there are great places to stop for a quick bite. "Godzilla" is open 24 hours, with excellent pizzas and salads (kinds you may never eat elsewhere in the world!). "Happy Bar and Grill" is another place where variety and good service are a main emphasis.
If you ever planned on having a tattoo, Varna is the place to do it, professionally and affordably. While walking down town, ask and almost every young person will be able to point you in the right direction. There are award winning tattoo artists, who will create a masterpiece on you, for the price of a bootleg tat in the States or Western Europe.
Catching a cab in Varna will not be difficult, but you won't always pay the right price. There is one thing you need to remember to do before you enter the vehice...BARGAIN. In most cases the driver will have very poor english (or german, or russian) which will mostly consist of the numbers. He/she will probably agree to take you to your destination for 1/3 of the innitially quoted price. A place where you'll always find available taxis is the plaza in front of the Cathedral, no matter what time of the day or night it is. 
Bulgarians are known for their ability to have fun. For the most part they are cheerful and friendly people and they love tourists, because they realize their contibution to the local economy. Nightlife in Varna is probably the best in the country. You'll find hands down the best club for house and techno music in Eastern Europe "Comics Culb" during the winter. During the summer the names and the mode4rn locations change. During summer 2007 the best places are "Pasha", "Extravaganza". The crowd there will carry you even if you aren't the biggest fan of this type of music, you will become one. Masai club in Golden Sands has been visited by some of the world's most famous DJs like Josh Wink, Dr. Cucho, Pablo Ceballos etc. and it is almost a weekly occasion.
While in Varna, do not make the effort of looking for a fine dining experience, because your expectations may not be met, but if you are willing to be introduced to the traditional Bulgarian food, or have some sea food in one of the countless beach restaurants, you will surely not regret it. Mr. Baba is a restaurant close to the harbour. Great Service and wonderful menu. It is an old ship and the servers are dressed as pirats. Nice wine selection.
The beach in Varna is not the best, but you can have loads of fun if you find the right spot. The above picture displays the night lights on the beach and it is the place to be for locals during the cool Varna nights in the summer. You may see the occasional topless lady on the beach(Bulgarian women are very attractive by the way)! The following picture is from a beach just 10 km north of Varna. There is reliable and very affordable transportation there departing from downtown Varna every 10 min. Prepare to pay 25 lv. for an umbrella and two beach beds, but it is worth it. The prices at the beach restaurants and bar there is also acceptable, due to the fact that most of the hotels are becoming all inclusive and the tourist don't have the need to purchase anyhing outside of their hotel. To attract customers the competition there in noticable. There will be people in front of the restaurants trying to convince you to go in, and that could become quite annoying after an hour walk by the beach.
A great experience for the children in the city's Dolphinarium and while there don't miss going to the cafe on the summer terace which overlooks the pools where the dolphins reside. Only a glass will part you from those beautiful creatures. The Dolphinarium itself is not the most modern one and as far as known it hasn't been renovated in decades, but the show is still worth seeing.
Enjoy!