Plan your garden with your neighbors, if possible. This way you will all have a nice place to sit and enjoy morning coffee. Try installing a small sunroom-type roof that allows coffee during light rain showers. Do keep in mind that someday you could have a falling out with your neighbors and not be able to use their side of the garden. Plan the garden so that your major purchases are on your side, not theirs.
Planting columbine, honeysuckle, salvia, bee balm and soapwort will attract hummingbirds and butterflies. Keep the honeysuckle in a large pot to prevent it escaping and spreading into your neighbors' yard. Soapwort has a tendency to spread in rich ground, so pot it up as well. The rest of the plants are well-behaved and require only require periodic deadheading and thinning.
Paint your own outdoor art on waterproof plywood, or purchase art already made. Choose your plants so they match or flow with the paintings. Abstract paintings look nice when paired with mother-in-law's tongue, Harry Lauder's walking stick, polka-dot plants, toothache plants (Spilanthes acmella), passiflora, bamboo (Phyllostachys bambusoides) and starkly contrasting caladiums. Soft, country-themed art looks good with sweet alyssum, mums, hollyhocks, spirea, potted willow trees and violets.
Avoid planting poisonous species near your fence line. Your neighbors could have kids or grandkids that will eat the poisonous berries, leaves and flowers. If your neighbors keep a trashy, smelly place, try planting a highly scented vine to mask the odor. If you share a fence with your neighbors, make sure the plants you choose will not destroy the fence or drop litter in their yard. When planning the garden, try making it flow with both landscapes.