Hands down the Gillette Venus & Olay Razor ($11.99) is the best drugstore razor I’ve ever used. It’s moisturizing, you don’t need shaving cream when using it in the shower, and it allows for a quick cut-free close shave. The one downside is that the blades doesn’t last very long (they start to get dull after about four uses and the moisturizing bars wear off around that time as well). The razor is a little bit more expensive than other Venus models because of the moisturizing bars and because you don’t need to use shaving cream, but I find it to be worth the premium for convenience and ease when traveling.
On a side note Venus has designed their razors so that their cartridges fit all models, so if you have an older model you can just buy the cartridge refill pack for Venus & Olay and pop it on.