I've been to Figueres loads of times, and never done a tourist route, but the shops are great and it's quite relaxing if you don't need to worry about parking - just pay! Quite a 'French' atmosphere...However, at this link there is a walking route and also clear explanations and useful stuff generally.
The Dali Museum
What can i say, apart from book your tickets online so you don't need to queue. It's very quirky, as a museum visit very entertaining and not just a rainy day activity.
Sant Ferran Castle
Situated atop a hill, at the end of Pujada del Castell, this is a large military fortification built in the 18th century under the orders of various military engineers, notable among whom were Pere M. Cermeño and Joan M. Cermeño. It occupies a surface area of 32 hectares within a perimeter running 3,120 metres, while the tanks under the parade ground can hold 10 million litres of water. Sant Ferran Castle, which could hold 6.000 men, is a first-rate heritage feature, the largest monument in Catalonia and the largest ramparted fortress in 18th century Europe. In the month of July 1997 it was opened up to the public on a regular basis with a guided visit service to show the fortress features. Its enormous size, sophisticated building techniques within the sphere of the period´s military engineering skills and its excellent state of preservation make a visit to Sant Ferran Castle a magnificent experience.
We visited this one sunny winter morning and it was a worthwhile visit although at the time there were no guided tours and not much information around. It's good for a walk at the very least and there is a little cafe for a refreshment. Actually a very interesting site and worth a visit while in Figueres. Combines well with a visit to the Dali museum in the afternoon (a must as they say).
Places near Figueres
A visit to the Monastery of Vilabertran, the medieval village of Peralada with its' castle and summer music and dance festival, Castelló d'Empuries and the citadel of Roses are all recommended options.