Personally, I like Prospect Heights and Bed-Stuy. Both have very attractive properties on varying blocks. The thing with Brooklyn and especially the Fort Greene, Clinton Hill, Bed-Stuy, Prospect Heights and Crown Heights area is that you can live in the area, get a nice apartment in a nice section of the neighborhood and never experience anything negative. You can also end up on a block that has consistent issues. In Bed-Stuy, I would preferably stay closer to the Fulton Vicinity...MacDonoguh, Macon, Decatur, Bainbridge etc. Those blocks have basically catered to more professionals then blocks further in like Madison or Hart Street.
Prospect Heights is really a very small area and it is very easy to get into a good location in that neighborhood. On Washington Avenue, it can get a little rougher and I believe the closer you get to Atlantic may not be ideal but all in all, a neighborhood that has good amenities and too me, fairly safe. There are complaints at times from people on another BB, but I believe they are centered around certain buildings in Prospect Heights and some things that have occured around the Franklin Avenue Station, as well as on Washington. As a note, Franklin Avenue is an express stop but it is not the stop for Prospect Heights. The Prospect Heights stop is basically a local stop on the 2 or 3 train (Eastern Parkway | Brooklyn Musuem or Grand Army Plaza) or the Seventh Avenue stop on the Q train. Even the Botanical Garden stop on the shuttle is actually in Crown Heights.
And to be honest, I don't know how many safety issues a woman would have in these areas so I probably am not the best one to respond, as I rarely see women having any real safety issues in the neighborhoods, as long as basic rules are followed like catching a cab when you are coming home late at night or having someone meet you at the train or bus stop etc. I cannot respond to catcalls or someone yelling "Shorty can I talk too you for a minute
", since that occurs all over the city and if that is considered a safety issue, then I would not look into any neighborhoods that I mentioned because it will eventually happen.
The best thing to do though is to explore the various neighborhoods and see how comfortable you are in them, then you would know which ones are worth looking into.