Can I get off a train, then on again later, for the same destination?

Can I get a return ticket to one city, get off at a stop along the way and see the sights there for a couple hours, then get back on the train and continue to my final destination all on the same ticket, or would that not be allowed?

Yes.  You just need to stay on the specified route you bought the ticket for, and use it in the same day (usually).

It depends on the type of ticket. According to National Rail:

Some tickets allow you to stop and restart your journey en-route.

    Anytime Tickets - you can break your journey on both parts of the ticket.
    Off-Peak Tickets - generally you can break your journey, except if the restriction associated with the journey says that you can't - please check when you buy your ticket.
    Advance - Break of journey is not permitted on Advance ticket, unless you're advised to change trains on your reservation confirmation.