We'd like to transfer some of our savings from euros to dollars. Is there any tax liability on such a transfer besides whatever interest it may earn once in the account? Also, does anyone have any advice on the best way to transfer between Europe and the US (lowest fees, etc)?
If you're US citizens you should have already paid income tax (outside any double taxation limits) to the IRS when you earned the money.
You haven't said which country in Europe. In the UK Citibank allows you to open a dollar account so you can exchange pounds whenever the rate is better, then send it to the US when you need to.
You need to ask your banks how much they charge for sending and receiving wire transfers. One site which may be useful is
http://www.fxcompared.com/Alternatively if the amount isn't too big you can just use cash? I do, but only because I travel a lot anyway so I don't need to carry large amounts which could raise suspicions.