Luckily, Bali is pretty compact, in terms of accomplishing what you want to do. If you get an early start (I'm assuming you're going to be somewhere near Denpasar/Kuta/airport), like 8:30 AM, you can see the Barong dance in Batubalan on the way to Ubud. It starts at 9:30 AM, but not sure exactly what days. From there, Ubud is another half hour. It's the cultural center of the island. The intersection between the market and the palace in town is nuts, but it's quiet, beautiful rice paddies once you move a couple hundred yards off the road. From Ubud, you can go north through Bedugul, with a stop there to check out the temple by the lake. Beyond Bedugul, you'll drive along a ridge that will give you some great views. Continue the drive and drop off the north side of the ridge, and you can do the short hike to the waterfall at Munduk. If you go a bit further, you can stop in the town of Singaraja.
'Course, this is one of a bazillion trips you could make. Any hotel can put you in touch with a driver/guide. Make it clear that you will not accept a guide who takes kickbacks from certain vendors in exchange for delivering customers. A full day should cost a couple no more than $40 plus your meals, entries to attractions, etc. You may or may not be responsible for your guide's lunch, depending on the arrangement.
If you're looking for a hotel near the airport, my suggestion is the Green Garden Beach Resort and Spa, which is actually about a hundred yards off the beach, and doesn't really feel like a spa, in Kuta Beach. Great hotel prices here:
Bali hotel Green Garden Resort & Spa hotel Kuta Beach discount hotel in Bali Green Garden Resort & Spa hotel
Five minute free shuttle to/from airport. If you have two nights in Bali, or if your departure flight from there is not early morning, you might consider staying in Ubud. You could take in either the Legong or Kecak dance in the evening. Lots of reasonable hotels and restaurants. I can share some info.
Enjoy!