I have a Grom and am around 5'-4" or 5'-5". I think it's a great bike to start out on (or stick with). I might buy other bikes, but I'm never getting rid of my Grom.
What most everybody has said here is true. It's about 9 HP (not much power at all) but it's fun because I just like being on 2 wheels. It does somewhat struggle up hills when compared to a full bike, but it's faster than a moped. I LOVE that it's so lightweight. It weighs less than my old 50cc scooter. And like a dirt bike, I can almost lay it down on the ground and pick it back up.
It does matter what you intend to use it for. If you need to go on the freeway for a short sprint, it's possible, but I don't use it that way and would advise against it.
The good: I really like the instrument panel - same one on most of the sport hondas that I've noted. It's cheaper to maintain than a full size bike cause it uses scooter size tires, etc. And my gas mileage is about 85 miles/gallon last time I checked.
The bad: The front suspension is not so great and I plan on updating that some day with stiffer fork springs. But it's not so bad as long as you respect that while riding. i.e. don't jump your grom stock or try to ride into potholes for fun.