I've collected a lot of water bottles over the years. From the cute ones that have cost more than I'd like to admit (and normally end up leaking in my purse) to the promotional ones from the bank or my alumni association, I've tried and donated more than I can count.
When I travel, the most important factor (above cuteness and ability to keep my water chilled for hours) is saving space. Which is why I always pack my Vapur water bottle.
I've had a Vapur bottle for years, starting with the one without the filter that rolls up completely to fit in whatever corner of free space is left in my carry-on.
But my new pick is the Vapur bottle with the built-in filter. Yes, it's a little more expensive, but having the added filter makes it a solid choice for me. That way I don't have to worry about the quality of the water in the airport drinking fountain or filling up the bottle at the sink in my hotel bathroom.
This is even more important if you like to camp, hike, or backpack. The filter removes 99.9999 percent of waterborne bacteria, and can be used as a straw in addition to being used in the bottle.
It might be overkill if you just need a water bottle for the gym, but it's ideal for travel.