To east side: 32 st and 1st ave from port authority nyc -fastest way
 

I am visiting my mother in NYC. She lives between lexington and 3rd ave on 32nd st.

What # bus or subway would take me the closest to her apartment? I cannot make out the

MTA bus map gibberish. I hope that I can get close to her because I have to use a cane.

Thank you and I wish you well.

Take the S (crosstown shuttle) from 42 St to Grand Central. There change to the Lexington Ave line of the subway and take the local (6 train) south to 34th St station.

The fastest and easiest way is to take a taxi. Otherwise, walk to Times Square and catch the Shuttle to Grand Central. Then walk to 2nd Avenue and take the bus diwn 2nd Avenue. It stops between 34th and 33rd. If you take the Select Bus, pick up a free Metrocard transfer before boarding.

All ways require some walking.

The shuttle is essentially worthless. You end up walking at least a long block (I think somewhat more) at either end. Take a taxi.

IMHO a taxi is the obvious answer - esp if you use a cane. But the OP did ask for public transit.

A less fast and but stairless way would be to take the crosstown bus on 42nd Street near 8th Avenue to Second Avenue and transfer to a downtown Second Avenue bus. However, the crosstown bus will probably move very, very slowly as it travels through busy Times Square and passes Grand Central.

I also suggest a taxi.

I agree that in your case a taxi would be best.

If you prefer to take public transit, then I agree with ellenem's suggestion of the crosstown and downtown buses.

The train is not really convenient and will require stairs and a lot of walking.

I must admit that I missed the cane issue. If you really need/want to use public transit, the only viable option is A/C/E train to 34th Street and then the M34 or M34A bus to Lex or 3rd Avenue and then walk only 2 blocks. This is not at all fast but is the only way to save steps.