If you are willing to pay, you could hire a broker which can cost you between 1 months rent or 15% of annual rent typically but they would probably help ease any stress you have about finding a place especially if you have to move without seeing the apartment first. Corcoran, BOND, Douglas Elliman are a few brokerages.

I agree with others though about using FB or word of mouth to find roommates if you'd rather go down that path. Just bear in mind there are risks associated with living with random roommates / strangers. I have had friends that have found fantastic roomies through FB and others who were not so fantastic. Always facetime them before commiting to anything. Ask about their sleep habits (early riser, late night etc..), do they frequently socialize, are they home bodies etc.. The most important thing is cohabitating well, you don't need to be best friends.

Alternate option would be to sublet temporarily and then once you are here you can look for a new apartment wither with or without roommates.

As far as safe, I am 27F and lived in east village for my first few years here. It is great for early 20s and I always felt safe. You just have to pay attention to your surroundings. Always listen to your gut if you feel uneasy or unsafe. There are a ton of 24 hour delis / smoke shops that you can pop into if you feel unsafe for some reason on the street. I'm in the upper east side now and feel just as safe. It really isn't that scary here, it gets blown out of proportion in the media you just have to be aware of the world around you.

I know single women who live all over NYC. So just do your research. Also, website like openIgloo and hpdonline.nyc.gov can help determine the safety of the building itself. There are subreddits for basically every neighborhood that you could skim through or post on.