Bryce is a relatively small park and can been seen in a day or two. The Lodge right in the park is the best place to stay since you are within walking distance to the overlooks. The nearby town of Bryce has many hotels and restaurants and is just outside the park.
On the way up towards the park from Kanab or Zion Park on Highway 89 in Orderville there is a bakery/cafe called Forscher German Bakery:
The classic hike starts at Sunset Point. From here you head down the Navajo Trail, along the valley floor which connects with the Queens Garden Trail before ascending to Sunrise Point. It's a three mile hike that takes you through some of the best scenery in the park. You can do the hike in the opposite direction but it involves a steeper hike back up to the rim.
Just before you get the Bryce Canyon on Highway 12 you will drive through a short rock tunnel and will soon arrive at Red Canyon, a miniature version of Bryce. There is a good visitor center and several short trails you can hike before reaching Bryce Canyon further up the road.
Cedar Breaks is about an hour and a half west of Bryce and is well worth a quick visit. Unlike Bryce you cannot descend into the canyon, but a hike on the Rampart trail which runs two miles along the rim and is relatively flat at about 10,000 feet elevation. The part is closed well into the spring due to heavy snowfall.