It is highly recommendable to visit a fitness center from time to time. To stimulate muscles you normally do not use very often is an important step to archive a perfect physic and better performance in any sport. From Cardio to high-intensity training you can do whatever you have to, to get in a better shape.
The most effective training is if you isolate different muscles and do the exercises slowly as you go. Try to pay attention to your body while pushing the limits. Bad weather is one more reason to enter the gym. If the gym is within your reach walk, there to discover the surroundings a bit and take a slightly different way back home. This way you might even skip your warm-up or cardio session at the gym, where you can concentrate on other things.
It is very likely that you will encounter different machines while visiting different fitness centers, which makes your work out more varied and fun. Some fitness centers have saunas, Turkish baths or even a spa to speed up your recovery and enjoy your holidays to the fullest. Doing a quick google search you will find all the gyms near you and you can even visit different gyms during your stay in the city. Maybe you meet other travelers or like-minded people to crap a coffee with right after your training.
Gyms usually issue day, week, or month passes which are great for travelers. If you spend 2 hours in the gym you still have 22 hours to recover and explore your surroundings. Think about it!