After returning from a two week honeymoon in Hawaii (1 week in Maui & 1 week in Kauai), I can tell you that the Kauai Beach Club is a joke of a resort. The customer service is so poor, in fact, we ended up leaving after two nights and transferring to the Hilton. Aside from hundreds of screaming kids, incompetent--and unconcerned--hotel staff, and outdated amenities, the resort itself is just fine. That being said, I would suggest leaving your room as much as possible.
When you do leave, there's a bunch of activities that you should consider.
Definitely take a road trip all the way north . . . the road ends at a beautiful beach (Ke'e) with fantastic snorkeling and hiking trails. Be sure to get there early because parking fills up very quickly. If you want to go on the entire 22-mile round-trip hike, take lots of water.
On the way back, be sure to stop at the Kilauea Wildlife Refuge and Lighthouse. It costs $5 a person to get in, but the views are worth it. You'll see all sorts of oceanic birds, including the red-footed booby, and if you're really lucky, you'll spot a Hawaiian Monk Seal sunbathing. There's only about 1100 of these seals left on the planet, so it's a treat.
Another activity you might be up for is driving and hiking through Waimea Canyon. There's a strenuous hike there called Kukui Trail that takes you on a 2300 foot drop in elevation in just 2.5 miles. Scenery there is amazing and there's no comparison. The bad part is coming back to the top. Bring plenty of water.
My wife and I also took a rafting ride along the Na Pali coast. It was a 5-hour event, cost $119 per person, and was phenomenal. It takes you past soaring cliffs, gorgeous waterfalls, and numerous arches along the undeveloped coastline. We saw plenty of dolphins swimming with us, sea turtles, birds, goats, etc. We went with Kauai Sea Tours out of Port Allen and they provided lunch and beverages. You also get to snorkel for about 45 minutes on a nice reef in Na Pali.
Poipu Beach is another great place to visit. Good snorkeling that's east to access, a great beach, and a more luxurious part of town.
Aside from all this, be sure to go to Scotty's (North of Kapaa) for dinner one night. Get there about 6-6:30 and you'llsee the ocean at its calmest from the open air seating. It's a great location with incredible bbq. Go hungry . . . the servings are huge.
Hope you have a great time out in Kauai! Don't let the hotel ruin your stay!