Where can I watch an ice hockey game without paying too much
Check out Ticketmaster. They sell tickets for Rangers (typically rather pricey) and Islanders to see if any tickets fit your budget. I haven't been to Barclays Center where Islanders play so I can't say if the cheaper tickets have a bit of obstructed views or not.
Depends on your definition of "too much".
There are 3 pro hockey teams and a few college hockey teams and there are probably some high school hockey teams as well. I'm sure at least one of those will fit your budget.
We are a family of five on a 5 day trip to NY and I would like to see a game but not fussed about the 'pro-standard', just want to see a couple of teams playing a decent game. I have seen there are a few teams at Chelsea Piers of an evening - would this fit my bill?
Jeanette is right. If you tell us your budget and dates we can give you solid answers instead of just wide ranging suggestions.
While I agree with Northern Traveler that the Chelsea Piers teams are amateur, it may fit your bill if you are just wanting to see the game played. There are some NYC high school teams (18U AA, 18UAAA) that are quite good, and the games at Chelsea Piers would be free. Are you looking just to see a decent game played, or for something more? Agree that dates would be helpful.
Your dates would be most helpful because some games might be more in demand.
The cheapest seats I can see that aren't resale for a random game for New York Islanders in January is $29 plus booking fee. This is really reasonable. Having been to see New York Rangers too and going to the Islanders in December the Islanders tickets are much cheaper and easier to get.
I see going to the hockey as being a night out as it's not just the game. Hope you find what you're looking for.