As for the unobjective, unsound reasons I skipped town, well, besides a general sense of Manhattan winter cabin-fever malaise (seriously, I'd estimate that this is how I've spent the last two months of my life: 50% studio apartment, 30% Glamour HQ, 10% Craftbar, 10% restaurants near Craftbar), I'd realized a few weeks ago that I was at a point in the year where I needed to reassess and regroup—on everything: relationship, career, ambitions, projects, personal goals, life in general. For me, without going into too much/TMI detail, 2014 was a year marred by uncertainty—and 2015 wasn't starting off all that much better.
In my (limited years of) experience, I've found that one of the most effective ways to get perspective is to remove yourself from the situation—even briefly. And while getting away with your significant other or taking a long weekend out with the girls can be chock-full of memory-making good times, being alone in an unfamiliar city with just a small suitcase of your belongings and an iPhone as a dining companion effectively strips away all the noise and stuff from the everyday grind—and leaves room in your day (and your mind) to remind yourself who you really are.
You don't have to go somewhere remote. Seriously, if you need to retreat to a cabin in the woods or do a full-on Eat, Pray, Love pilgrimage, go for it, but sometimes it's refreshing to just get lost in a sea of unfamiliar faces. If you don't live in New York City, come here—it's vast and anonymous. I've done a few solo trips to Vegas—the strip is surprisingly safe and single-traveler-friendly—and some weekends I'll wake up Saturday mornings, hop a bus, and take myself to Philadelphia for the day. Other cities that I've personally found very solo-female-traveler-friendly: Miami, Los Angeles, Chicago, London, Paris, Shanghai, Tokyo—in broad strokes, I like a walkable city and places with robust public transport and friendly/safe taxi drivers.
Be safe. You won't be able to relax and think if you're constantly worried about personal security. So, first and foremost, when you're traveling alone, plan the logistics of your trip based on the principles of safety and convenience—book a well-staffed hotel in a safe neighborhood where you'll be comfortable venturing out on your own. Lots of good, close-by dining options can't hurt either.
Wander around, do only what you like. One of my favorite things to do in unfamiliar cities is hailing a cab, getting dropped off in the middle of a shopping hub, and wandering around for hours, either chatting with local shopkeepers or spending the afternoon pretending I don't speak the language and talking to absolutely no one. You know how some people go off into nature to clear their minds? Yeah, this is my version of it—urban hiking. Directionless, consumer-behavior-ish meandering is a great way to tune in to the present (being in the now), relax your mind by allowing it to process pretty meaningless data (all the new stuff you're seeing), and, also, acclimate you to new surroundings.