There is a tourist office on the stradun. You will find it on your left side about 75 meters from the pile gate.
The information you can get here is however a bit limited, and in regards to boattrips to the nearby islands it is often not the best price that they offer.
Okay, my fondest memory . . .
Like many people I would guess, my favorite memory of Dubrovnik is hanging out on Stradun and just relaxing at the cafes with a cup of coffee and really absorbing the atmosphere. Since my body was still recovering from my unfortunate incident in Split, I spent more time than usual, just relaxing. I even bought a book and finished it off before I left town! If I wasn't on the street, I was in a restaurant or bar getting to know some of the locals. Most of them were polite and a little reserved at first, but once you show a little interest in them, they will reciprocate and want to know all about your trip and what you're doing in their country!
A good guidebook is priceless
The 2nd edition Lonely Planet Croatia guidebook is priceless if you are traveling in Croatia for more than a few days. It is really worth its price, and the information you will gain from it will make your travels in the country ever so much more memorable and meaningful.
From the Pile gate of the old city, it's just a short walk to the Lovrjenac Fort. This is a fine monument and a wonderful place to take photographs of the whole city of Dubrovnik. It's pretty deserted, being off the tourist trail, but worth a stop. There is a small admission fee.
The easiest way to explore nightlife of Dubrovnik is to walk through Stradun in the evening. It is the main street, full of restaurants,bars and souvenir shops. It's crowded,but you'll always manage to find nice seat with a view. At night you'll find different parties in little streets and squares near the Stradun. Nothing special,there are all kinds of people there.