Mardee,
Yes Texas TM is right- there is at least one, I think two posts all about Manchester as a destination. I just can't find them!!. The search function is not sufficiently sophisticated.
Whether you could squeeze it in on the train when you are in Liverpool I don't know. There are various routes across from Liverpool but most will do the 40 miles or so it in under the hour. The northern trains at least you should get in advance for between £3 and £4 each way (with a railcard as little as just over £2 each way)- less than the cost of the petrol, let alone the parking.
One of the things we might have missed off (if we can find the threads) is IWM North. Lots of people visit the various branches of the IWM in London, but I don't think I've read on here about anyone going to IWM north at Salford Quays. Dead easy now with the new tram line that stops outside.
If you were really lucky Mersey Ferries do seasonal day trips from Liverpool to Salford Quays- up the Manchester Ship Canal- which delivers (or did) ocean going ships to the heart of Manchester, including passenger liners in it's heyday. It's an all day trip with bus return. Nowadays ocean ships don't really get beyond Warrington (where there is also a transporter bridge- one of only a handful in the UK). But there are also little short trip boats from the Quays up into the City Centre for the start of the Trans Pennine canals which cut through the heart of the city centre.
Canal Street in the City Centre is a thriving night time economy, famously Manchester's gay village, and a stone's throw away is Chinatown- one of the bigger Chinatowns in the UK.
There's things like the L S Lowry centre at the Quays- the well known painter. Again I think that was missed off the threads. As well as the museum there is a visual and performing arts centre at The Lowry. It's actually a good base for Manchester having tram lines on both sides of the canal. Both the BBC and ITV have regional centres out there now. In fact all BBC national news is now broadcast from Salford.