We have visited NY a number of times but have always stayed closer to the Upper East side. This time we are staying on Greenwich and 10th.
What would be the approximate cab cost from LGA?
Any other (less expensive) way?
We will have only over the shoulder carry on bags.

With fair to midlin traffic about 30 bucks. Ask the driver if he knows the back way to the 59th Street bridge.

Directly from MTA site:
You can also take the Q33 bus to Roosevelt Avenue-Jackson Heights or 74th Street and Broadway in Jackson Heights Queens. If you get off the bus at Roosevelt Avenue, you can catch the E or F trains into Manhattan. If you get off the bus at 74th Street, you can catch the #7 train heading into Manhattan. This train stops at Times Square where you can transfer for free to another train to take you anywhere in the city. For a detailed subway map, visit the MTA's page.

The E, F, will leave you at the West 4th Street Stop or at Times Square you can get the R and get off at 8th Street.

Either way, it will take a bit of time.

thanks Adu,
I think we'll take a cab... as you said, the other options are too time consuming!

Make sure you are clear about whether it it Greenwich Avenue (which goes cross town from 8th Street and 6th Avenue over to 8th Avenue) or Greenwich Street, which runs north/south and is on the far west side of the West Village.

nyccabfare.com and hopstop.com will estimate the cab cost. You could also order a car service for a fixed price from dial7.com or similar if you're arriving during rush hour which can run up the meter.

thanks all for helpful info.