It sounds strange, but the Vita may be my favorite system I own. I travel a decent amount for work, so it's really nice for that. My favorite thing about it is probably the quality of it. I have the original OLED WiFi model, and it just feels solid. It runs smooth as butter too. I love how I can pop out of a game, suspending it, go and check my trophies or a game guide online, and pop right back in (Note you can't do this on all games as some games requiring more horsepower like Borderlands 2 disabled it). One time I suspended the whole system and forgot I was in the middle of a game, and 2 weeks later picked my Vita up and picked up where I left off.
The screen is great, controls are good--about as best as I would expect dual analogs on a portable to be. I hear the newer Vita is more comfortable, but I can't speak from experience. I have experienced some hand cramping on long sessions with certain games on mine. The front touch is useful, back touch not as much as it's difficult to be accurate with it.
If done well from a controls standpoint, Remote Play with PS4 is an awesome feature. It works shockingly well. I have my PS4 on a hardwired connection at home (30 down/5 up internet) and my Vita in decent WiFi (5 down, 1 up or better) when playing usually. I hear PS Now is great on it too, but I haven't tried.
As far as games go, there are plenty. Since handhelds are more popular in Japan, you'll find no shortage of JRPGs. I won't list every game I recommend here, but I personally have enjoyed Persona 4 Golden, Uncharted: Golden Abyss, Freedom Wars, Danganronpa, the Metal Gear Solid Collection, LittleBigPlanet Vita, Sly Cooper Thieves in Time, Borderlands 2, Gravity Rush, Tearaway, MLB 15 The Show, Hot Shots Golf: World Invitational, and PlayStation Classics.
The main downsides to it are the cost of the proprietary memory cards and the lack of love over the years from Sony and third parties. That doesn't mean there isn't plenty to play on it though. I ended up importing the 64GB memory card from Japan. 
