IThe amount that I want to spend is tentatively $2000, but I could see myself selling the Tamron, and forking up a little bit more to get a 6D w/ 24-105mm f/4 IS, but then again, I don't know if I could justify the price for essentially a "first-time" DSLR. The GPS feature will be great for traveling being that I will be in 7 different countries while I am in Europe.
this is the best option in my opinion
the tamron 18-270 is possibly one of the very worst lenses ever made by anyone
even though you have the 50 1.8 I would still recomend the 40mm pancake on the 6D just because that lens on a high iso FF camera is such a nice light walk around combo that would be prefectly suited for travel and 50mm can be a little tight also you need to stop the 50mm 1.8 down to around 2.2 anyway
The OP said he is going to buy a 6D, this is a full frame camera. The Tamron 18-270 will not work on the FF body. For Full Frame bodies like the 6D he should be looking at the Tamron 28-300mm XR Di VG, This combo would make a excellent walk-around lens for European travel. I would also take a ultra wide angle too. I think a Canon EF 16-35mm 2.8L II would be great. The building are so close together, and close across from each other a ultra wide is needed to get good shots. Like the plaza in Rome with Trevli Fountain is very tight with close in buildings all around.
I did see an ad for the 6D at a ebay store for about $1500, body only. They also have a new 7D for $859, but this is a crop sensor, and the Tamron 18-270mm will work fine with this camera. I own a 18-270 and it is a great walk-around lens, for Europe, I would get a Canon EF-S 10-22mm for those close in shots.