Hey there, congrats on the new purchase. Cool deal making a road trip out of it.
Havasu is a beautiful lake. 1 day to check it out is a tight timeline so I'll keep it short... My advice... Launch at Havasu Marina on the island, idle thru the channel and check out London Bridge, go up river thru the gorge (one of the most beautiful spots) and keep heading up until you go under the I 40 bridge, check out the Topock Marina to your right and Pirates Cove to the left. My favorite is Topock but some young single bucks like you might like Pirates better. Don't drink too much at either place because Havasu is patrolled regularly. Now, IF you still have some time, head back down in the direction you came from and go around the island where the London Bridge is (stay right), continue on and check out Copper Canyon; it's easy to find on the right side because of the buoys near the entrance.
There are countless other gems to discover on this lake but that would be a great start.
Lodging... Island Inn Hotel would work, it's right next to the launch ramp:
1300 McCulloch Blvd N
Lake Havasu City, AZ 86403
Have fun.
Steve-O