KellyeK given your range of interests you would have no difficulty in filling a five-day stay within Berlin. The city is vibrant, historically relevant and is home to a superb range of museums, galleries and community activities. You will also have good weather in June and should be able to enjoy the many gardens located within the city.

If you need a break from Berlin then I would recommend Dresden which is accessible by train ~ 2 hours each way.

Berlin is surprisingly affordable and you should have no trouble finding accommodation to suit your price range.