My best guess as to what's going on is that she's trying to meet a new friend in the area, just like she told you she was.
As someone who has been very insecure in past relationships, I can understand why you might be suspicious, but you have to figure if she moved 500km and gave up all her friends just to be with you, chances are she's not going to give you up that easily, so just relax a bit.
Granted, that can be a bit difficult, so I'm going to give you some advice about how to handle this kind of thing in the future, based on what has worked for me:
DO:
- Talk to her when you are worried. Tell her that you're worried. Tell her that you trust her, but you're confused about why she did (whatever has you worried).
- Believe what she says.
- If what she did makes you uncomfortable even given that she's not up to anything, tell her that it makes you uncomfortable, tell her why it makes you uncomfortable, and see if you can work out a solution so you'll be comfortable, or she'll stop doing it.
DO NOT:
- Do not go behind her back.
- Do not read her email, her chat logs, or her diary, unless she shows them to you first.
- Do not assume she's doing anything wrong.
- Do not ask her to tell you the truth after she's already explained herself.
Asking the internet for advice like you did isn't likely to hurt anything, but it's also not terribly likely to help you either.
First and foremost, though, what you should do is work on correcting your own tendencies of distrust. Relationships require honesty, communication, and trust from all involved people. They can also take a lot of work at times, but the result is worth it.