San Diego is full of a fast moving base of people. People often switch apartments yearly or come and live for only a year or two. Downtown is best compared to places like La Jolla (which is near UCSD campus) or El Cajon (near SDSU campus) because there are always apartments available because they aren't occupied by students who are all on the same 9mo rotation; plus, there are plenty of high rises and houses that are split into multiple apartments. The nicest part of downtown to live in is north of Laurel St near 3rd Ave, but it gets a bit more expensive. Hillcrest is the more lively area of northern downtown. It is near Balboa Park, has plenty of night life, and is a really great gay community (really friendly people for a city). Cheaper places to live in the heart of downtown is 3rd Ave past Broadway. The city is cleaner and much safer than NYC (100 fold), so that isn't something you have to worry about. But, if you live in downtown, be aware that every year when Comic Con happens, you will not be able to park or drive for a week (it's mental). Best to live up north near Banker's Hill or Hillcrest.
Like I said before, avoid 15th or higher. That is where the heavy crime, homelessness, and drugs start.
Also, despite how cheap it is to live there, avoid South East San Diego. This is where San Diego's gang crime is heaviest. It is San Diego's Compton. Home to the Lincoln Park Bloods. See the photos below. Avoid this area at all costs, no matter what race or ethnicity you are. The good(?) thing about San Diego is that the city has an agreement with some of the LPB's white collar crime to keep the crime out of downtown in exchange for turning a blind eye. This makes downtown and the surrounding areas pretty damn safe with no significant gun crime, GTA, or muggings. There are a lot of homeless in San Diego--being from NYC, that is nothing new to you, I'm sure--but they are well taken care of by the city, so they aren't violent or disruptive and are often quite friendly.
Hope this helps. Enjoy San Diego. Most people who have lived there will agree, it is one of the greatest cities in America. 😃