Hi Erin,
Congratulations on your wedding at Walt Disney World!
It's very easy and convenient to travel between the Art of Animation and Pop Century resorts. The Generation Gap Bridge over Hourglass Lake connects the two in the center of the resorts, near the '60s section of Pop and the Finding Nemo section of AoA. Those rooms are very close to each other.
You also can walk between the two on each end of the lake, between Cars and the '80s on one end and Little Mermaid and '50s on the other. You can zoom in and out on the
Pop Century resort map to see the proximity of the buildings.
No matter where you are in either resort, it should be more than a 10- to 15-minute stroll to the other resort.
To get from the resort to Boardwalk, I would take the bus to Hollywood Studios, then either take the boat to Boardwalk or walk. The boat leaves from the front of the Studios and stops first at the Swan/Dolphin and then the Beach Club/Yacht Club enroute to Boardwalk. If you walk, the wide sidewalk will lead you along the waterway to Boardwalk. The walk is often faster than the boat, but neither should take more than about 20 minutes.
And, for your final question, yes, taxis are readily available at every resort and theme park. The fare anywhere on Walt Disney World property is usually less than $20, including tip. The only time I have paid more than $20 was from Animal Kingdom Lodge to the Polynesian (probably the longest ride on the property).
I'm a big fan of the free Walt Disney World transportation, but occasionally, it's nice to splurge on a cab for convenience.
I hope that helps in your wedding planning. Don't hesitate to come back to the Disney Parks Moms Panel with other questions as your big day nears. We're happy to assist.
Enjoy!
Wilma