Because the layout of downtown Playa is a rectangular grid, getting around is very easy.
The main east-west street, Avenida Juárez, connects Highway 307 with the town square, El Zócalo, near the beach. As it does so, it crosses several numbered north-south avenues that run parallel to the beach, all of which, interestingly enough, are multiples of five. Quinta Avenida (Fifth Avenue), the closest to the beach, is closed to traffic from the Zócalo to Calle 6 (and some blocks beyond, in the evening).
Playa del Carmen is pedestrian friendly and you can basically walk to everything. This is ideal if you are bringing a stroller. A bike is a fun alternative to walking; there are a number of bike rental shops at the north end of 5th Ave, some with trailers/ child seats appropriate for toddlers. 5th Avenue is stroller friendly, albeit a little bumpy due to the cobblestones. The streets other than 5th may be a little harder to navigate as the sidewalks here are not consistent and have random drops in elevation. Playa del Carmen also offers a network of bicycle paths, along Avenida 10 and along Highway 307 to Xcaret.
Car rentals are readily available at a number of locations at the north end of 5th Ave. Large companies, National, Hertz, etc. are convenient, as well as local agencies, which are generally less expensive. You can also rent a car at the airport. Remember to pre book a car with a car seat if you are not bringing your own in order to ensure availability.
5th Ave. (‘Quinta Avenida’ or ‘5ta Av.’) is a pedestrianized street and taxis are available at various intersections along its length. Taxis are reasonable so if you are sightseeing in the region, hiring a taxi for a day might be a good option as it will ensure your transport is waiting for you when you need it.
There are scheduled bus services to destinations in the region (e.g. Xcaret, Xel-ha, Tulum, Cancun airport, Cancun, etc.) and beyond depart from Playa bus station at southern end of 5ta Avenida and Avenida Juárez, which is near the Ferry terminal to Cozumel.
You can opt for the first class ADO bus departs hourly or so for tourist destination of Xcaret, Xel-ha and Tulum or the second class local Mayab Buses which also leave from Fifth Avenue station. Mayab buses stop more frequently en route and drop off alongside the highway to Tulum, requiring walking from the highway to the entrances of Xcaret or Xel-ha. When travelling with a baby or toddler the first class option is best. You will be able to stow your stroller on board the bus and will need to hold your child on your lap.
An alternative to the buses is to catch a “colectivo” van. These leave/return at Playa del Carmen from a location on Calle 2 between Av 10 and Av 15. Colectivos are cheap, government regulated, air-conditioned vans which transport people on Hwy. 307, which runs north/south along the coast between Tulum and Cancun.
Organized bus tours are also available from a variety of companies that cross the Riviera Maya & Yucatan. Ask at your hotel for details.