You should check out King's Peak. It has a pretty well established trail all the way to the top (although a bit brushy in the middle), and takes you through a gorgeous area. The first part is taking you through some dense forest, then you move in to alpine meadows and finally into rockier territory. There are few technical areas or those involving any real exposure. That said you are climbing very steadily and I recommend making this a 3 day trip (there is nice camping in the meadows). At over 6000m this is in the top ten tallest mountains on V.I. and the views are incredible.
My dad and brother climbed Albert Edward a couple of weeks ago and really liked the trip. They camped at Circlet lake for two nights, and judging by photos it's a really nice spot. If you just want a day hike it would be worthwhile just hiking into this lake (another option for a day hike is just wandering around the Forbidden Plateau area, Abandoned ski lodge and chairlifts = creepy)