One of my favorite things to visit on Oahu is the Waikiki Strip. It's safe, clean, there's live music, and a bunch of beautiful beachfront resorts line the strip. I like to drop in the different resorts and browse the shops, check out the pool, and take pics. The Moana Surfrider is one of my all-time favorites. It is a legendary landmark with a colonial feel. It's a hotel I've visited many times, but never stayed in. For amenities, great service, and beautiful views- check out the Royal Hawaiian aka "The Pink Lady". Now that place is special :)
As far as the cheapest month to travel to Hawaii, actually there are two specific periods to consider. These make up Hawaii’s low season. The first is in the spring, from the Easter break until the middle of June. The other half of the low season runs from September through the middle of December. I've been during different seasons, and never really found Hawaii to be packed. However, if you want the best deals, consider traveling during these times. You may even get an upgrade at some of the hotels! I was fortunate enough to snag an upgrade to an ocean-front room when traveling during the low season.
Quick note on my dress: It is cute and comfy- but boy does it wrinkle! Luckily I had an iron in my hotel room.
SHOP MY LOOK: