You can stay up to 5:59 AM with no ill effects. Just stay up to around 5 or so, then teleport back home and go to sleep, and you'll get no ill effects. You can stay up past 6 AM, but you'll get fatigued, and then sick if you do the same while fatigued. Use Cold Medicine to avoid sickness/fatigue and you can stop sleeping altogether (Micah is that awesome), but that's a tad expensive ;)
I usually stay up to around 3-4 AM fishing, then cook the fish (eat some of it if I need more RP). Good way of getting some extra cash and some much-needed cooking skill. Of course, early in the game you won't have the recipes or cooking skill need for some of the more advanced fishies, but all squids count. Or so I say.