Types of cameras that will work
For landscape photography, specifically, nearly any current digital camera--including those on smartphones--can do a good job. What you really need to worry about more is getting a tripod to use with it, and learning proper landscape photography technique, which generally involves using smaller apertures for a deeper depth of field, and reducing vibration for longer exposures (cable release, timer, etc.)
Camera specs to look for
What you'll want to look for are dynamic range capabilities, and resolution. And the resolution you choose should match the output format you plan to use. If you're only going to post online or send image around in emails, again, nearly any current digital camera will do. It's when you want to make big gallery prints, that you need to consider how many megapixels the sensor produces.
Features to look for
Personally, the only two features you probably really need to look for are full Manual shooting mode, so you can control the exposure settings explicitly. M mode generally comes with with what are known as the "PSAM" modes (Programmable Auto, Shutter-priority, Aperture-priority, and Manual). And you probably want RAW capability, if you plan to do your own post-processing to get the most out of the digital data. RAW lets you bypass JPEG compression if you want to.
Many people prefer a wider lens for shooting landscapes, but it's not a requirement--some folks shoot landscapes with tele lenses, too. But if you're getting a compact fixed-lens camera, 24mm film-equivalence (vs. 28mm or 35mm) may make you happier if you like shooting wide.
A final note on budget
For $400, I honestly wouldn't recommend going for an interchangeable lens solution, because you may only be able to afford the camera body, and not lenses to accompany it. For $500 and below budgets, I'd recommend a fixed-lens camera, and you may have to go used or lower-end if that budget also has to include a tripod of some kind. But with a smaller lighter camera, you could probably get away with a smaller travel tripod or evey something like a gorillapod or beanbag.