That's a good question. More people don't realize it, but Staten Island's one of the cheapest places you'll see in the NYC metro area. I noticed it said you were from NJ. NJ is much more expensive than SI and is even more than pretty much every borough of NYC, except Manhattan and downtown Brooklyn. I'm glad you've seen the economic advantage of moving in Staten Island.
Staten Island has much lower real estate taxes than NJ. For a split end home in let's say Middlesex or Union county, you could be paying up to 10 or 11 grand. In Staten Island, probably about 4 or 5. That money does get directly distrubited into the public education system which is why New Jersey's education is so much better than the Board of Ed. The Board of Ed only graduates 45 percent of it's kids, which is pretty embarrassing for it's city's affluence. Even if you did send your kid to a Catholic/Private school, you'd still be saving money. I know public school's aren't the issue for you though, so you wouldn't have to be burdened by the over taxes.
Unlike most of NJ, there are few community college type priced school's in NJ. I know one is in Trenton, the College of NJ. CSI is pretty affordable and is technically a university. Another advantage of living on SI besides it's real estate being cheaper is that your car insurance would be lower and if anyone works in Manhattan (or SI), you wouldn't have to pay that nasty commuter tax. The Express bus service in Staten Island is adequate and underrated for the most part. Most people on the island are either unaware or so cheap they take the train to the Ferry which can kill up to 2 hour's each way. Meanwhile, you could probably get to Manhattan quicker on an Express bus (5 each way as opposed to 2 each way - since you get charged in St. George for the train). You'd actually get the transfer when going into Manhattan, but if someone chose to drive to the Ferry they'd be paying for that.
One of the best ways a Staten Islander could commute to Manhattan could be this new way of taking the city bus into Bayonne. It'd especially be well for those in the Port Richmond area. They only make two stops in Bayonne, one being the NJ Transit rail. The ride is only about 20 minutes and is only 4 dollars to bring you near Midtown. The route actually starts out in Eltingville and would take about a half hour to do the whole run because it is a local bus service.
When you look at Staten Island, there are three area's. The North Shore, the Mid Island and the South Shore. The most populated of the all is the Mid Island, but it's also the biggest and the best part of the island to live in. Most homes on the North Shore are old. They usually range from 75 to 100 years old. Most of the new homes on the south shore are townhouses. The supply of homes on Staten Island has become so out of control, along with the amount of homes that have jumped on the market. It makes the property less profitable and it'll make people take longer to sell. Staten Island is a good place to own though. For New Jersey, it's probably not because of all the taxes' you'd be paying. You'd be lucky if you broke even after all the work and taxes put into the home.
I'd stay away from the south shore, even if you were planning on living in a split end home. I'd stay away from any townhouses, unless you have no other choice. You'd be better off renting a split end. Townhouses are not real homes. They're condo's or apartment's at best. The parking accomodations are usually not good. People are on top of each other. It's made it more vulnerable for kid's to start trouble on the south shore which is experiencing lots of rising crime, graffiti, car thefts and drug selling/usage especially.
For what's around CSI, those neighborhood's the other people on here recommended would work. Westerleigh is nice. Most homes in New Springville are pricey because of there size and there newer than most other homes on the island, but it's nice. Great Kills, New Dorp and that part of the island isn't bad either. I'd stay away from anything north of Clifton. Neighborhood's like Port Richmond, Rosebank and Clifton are decent, but overpopulated. The public transportation service with the buses are at it's best in those parts of the island though.
For a decent three bed room home that's built post-WWII, you'll probably look to spend in the neighborhood of 4 to 425. You can really negotiate now. For something that's more like 80 years old, you'll probably spend 300-350 varying on it's condition. More of those homes exist in older neighborhoods like Tottenville, Charleston and Richmondtown on the south shore and Port Richmond, Marinors Harbor and West Brighton on the North Shore. In general, geography doesn't really play much of a role when it comes to cost in SI. Certain neighborhoods that are run down like Stapleton with good geography actually cost less.
Neighborhoods I'd definitely recommend are Willowbrook, Graniteville & Clove Lake.