I am considering taking the Best of Eastern Europe tour in 2016. With the influx of refugees, predominantly from Syria passing through Croatia and Hungary, has anyone encountered any issues/problems on their travels through this area?
It's pretty hard at this point to predict what the situation will be in 2016, and if someone is having or has recently had issues they may very well be non-existent months from now. I don't think I'd worry about it if I was you, at least not yet. If you're worried don't plan anything you can't cancel. If you're on a tour it's definitely not an issue - a tour will be kept up on the latest information and will be flexible enough to make changes to avoid any issues that may impact the tour. That's why you take a tour, so you don't have to worry about things like this.
As previously mentioned, it's difficult to predict what the situation will be like in 2016. I wouldn't worry about it, as you likely won't be affected at all. The refugees in Croatia and Hungary are only using those countries as a transit point, and aren't staying any longer than they have to. You'll be travelling on a large, luxurious coach and shouldn't have any issues.
In addition to the fact that no one knows what the situation will be in 2016, you will be on a tour. This means that there is someone to take care of any problems; you don't have to figure things out on your own. That's exactly what the extra cost of the tour pays for, compared to doing it yourself - this kind of "insurance" that if there's disruption for any reason, someone else will handle it.
We did the Best of Eastern Europe in September 2015 with no problems at all. We saw some migrants being quietly processed from a bus near one border and after our tour on our way to Zagreb, the train stopped short of the Croatian border and we were bussed to the train station in Zagreb. No Big Deal. Its a fantastic tour! As someone else mentioned...that why you go on a tour...to have someone else worry about it. I would not hesitate to sign up...you will love it!
At the end of the September 1 GAS tour this year a couple from our group was taking the train to Budapest. Their train was cancelled because of the Syrian issues. They were able to get to Budapest by going through Slovakia instead of a direct route. This was after our tour, so I would chime in with the others. Take the tour. The Rick Steves team will take care of you. Btw, another couple on our tour took another RS tour after the GAS tour. She was injured in Florence and 2 different RS tour guides got her to the hospital and stayed with them until they flew home to have surgery. They aren't just professional guides, they are great people.