We are flying into Zurich on June 12 on our way to Basel for our river cruise to Amsterdam on the 14th.
With our limited time should we stay in Zurich and see what we can (suggestions) or venture out away from the city. Lucerne maybe?
Resonable hotels?
Any and all help will be appreciated!

Why even bother staying in Zurich in that case? I am not sure if you looked at the train situation at www.sbb.ch/en/home.html. There are hourly direct trains from the Zurich airport to Luzern in 62 minutes and 72 minutes with a change in Zurich HB main station with 12 min transfer time. Since you are with presumed to be laden with typical cruise luggage, just take the direct an hourly train.

We stayed in both Lucerne and Zurich last May and loved them both. If I had to choose where to spend just one day it would be Lucerne. Switzerland is a very expensive country so it may be difficult to find what you would consider to be a "reasonable" hotel, but because it is only for a night or two I suggest spending a little extra for a hotel in the old town or on the river.

For the average person not having been to either Lucerne will by far seem more romantic and perhaps fulfill the dreamy picture of Switzeerland perhaps etched in your mind's eye.

I would train to Stein Am Rhein, 1 overnight or just for the day

Another option if you can do an overnight, would be to train to Schaffhausen to stay 1 night, and take the boat down the river to Stein am Rhein and back to Schaffhausen, that is lovely!

Do a google image search for Stein am Rhein, it's just wonderful and about an hour from Zurich airport

Schaffhausen is a really nice Swiss enclave surrounded by Germany - situated north of the Rhine! You can walk a few miles on Rhineside paths to the Rhine Falls, very famous thundering water cascade and wrenwood's suggestion of the boat ride to Stein is great too - and very close to Basel, which is also a good look around - not all chemical plants!

I think it would depend on your interests.