wow man, that sucks. First of all, your grandma isn't your mom, so fuck her!
Lessee.....If you do sneak out, don't wear bulky shoes (duh), don't wear shoes at all. Crab walk to the computer, even if it means crab walking down a lot of stairs. If you hear her make a noise, like "sNNHHK!", really violently, and it sounds like she's waking up, stay silent. Absolutely silent. You have to be a ninja about this, see.
If you are caught, say you couldn't sleep and you are checking your email. Or some other belivable story. Say you need to get a glass of water, and the computer made a weird noise and you went to check it out. Lie your ass off. Remember, the worst that can happen is that you get an early bedtime, which you can disobey by sneaking out late again.
Seriously though.....it's summer, this isn't your grandma's house, and just cause she's the gaurdian doesn't mean she can be an asshole about it. If possible, make a lie that involves your mother's athourity, like say you got a phone call from her, you talked it out with her, and she agreed to let you stay up till 2:30, max (I go to bed normally around 1:00, that's all I need)
You'll get better at this, trust me. My friend and I started sneaking out of the house this year, and it's fucking amazing. Scary, but sick as fuck. You just have to be a sensible ninja, and be quiet as an ant's fart.