Until a few years ago, the Forum area in the centre of Rome was open and free to get into - it's now been fenced off and have to pay, but the ticket is the same one for the Palatine and Colosseum. I've only been back there once since this was done, and found the whole area a maze of gates, bottlenecks and queues - not a good development! That was in late May/early June, and I'd definitely suggest avoiding this period if possible. The best time for a visit would probably be late autumn, when the weather is still fine but the crowds aren't so overpowering.
The gate to the Palatine just south of the Arch of Constantine still appears to be the best for getting tickets, although even there I found sizeable queues. The ticket itself is good for two days - but everything's closed on a Monday, as mentioned above, and it's best to check the Colosseum's not closed for some inscrutable Roman reason (I fell foul of this one on my last visit too...)
Having said all that, some of the newly-opened areas are very fine: the Nova Via running down into the Forum past the Atrium of the Vestals (although you can't actually get into the Forum that way :evil
, and the crytoporticus on the Palatine.
I'd second (or third?) the recommendation for the Palazzo Massimo alla Terme (National Museum of Rome) too - some great statuary etc, and if you can't make it down to Pompeii to see the stuff in situ, there are some reconstructions of Roman rooms with original wall paintings, including the famous 'Garden of Livia' frescoes. Very nice
