There are 3 things to do in Budapest when its raining:
1. Go to a bath house
2. Visit a museum
3.Get drunk in a pub
Choose the spa!!
Budapest has plenty of bath houses both Turkish and regular ones with mixed audience. Make sure you spend enough time to relax your muscles and refresh yourself. Spend 20 minutes in the hot tube up to your heart level, then go to the soundproof chilling room and relax for an hour. Refresh yourself in the cold pool and go to the dry sauna or the steam bath for 5-10 minutes. Refresh yourself in the ice cold pool then enjoy the other pools and facilities (e.g. massage) of the bath house.Enjoy!!