San Antonio is famous for the Alamo, but the city also has four other Spanish missions, all in much less urban settings south of the Alamo and downtown San Antonio.
You can certainly drive between all four of the missions - Concepcion, San Jose, San Juan, and Espada, but you can just as easily bike between them.
The Mission trail is about a 15 mile round trip if you do all four missions - if you want to make it shorter for a family trip, cut out Mission Concepcion, because that mission requires some bike lanes on city streets.
The Leon Creek Greenway is being expanded - for now, the main section goes between Bandera (Mainland) and Babcock in west-northwest San Antonio through O P Schnabel Park. The path is paved, and wide enough for walkers, bikers, and runners to share if everyone is being polite. Along the paved path, you will see lots of unpaved trails going off into the woods for exploring.
San Antonio's marathon got a huge boost when Competitor/Rock and Roll took over the old San Antonio marathon and created the Rock and Roll San Antonio marathon in November. November can still be kind of a crap shoot for weather in South Texas, so this may not be your fastest time.
The best running calendar is at http://www.rogersoler.com/sbr_events.php
Also check http://www.centexruns.com/ for even more listings - they pull in races from the Hill Country, San Antonio, Austin, and north of Austin up to Waco.
The Rock and Roll San Antonio marathon has quickly become one of the biggest marathons in Texas after the Rock and Roll Marathon company took over the old San Antonio Marathon. The Rock and Roll San Antonio marathon is a little early for a Texas marathon, so you take your chances with the weather (it could be 80 degrees, or it could be in the 50's). San Antonio is a great city for tourism, with lots of visitor attractions and different options for hotels.
This first-year run in 2010 is put on by Sea World San Antonio as a fundraiser for conserving wildlife. Both the 10K and the 5K are held entirely within the Sea World Park, although the 10K sees more of the park (both spend the first 2 miles or so in the parking lots and access roads, although you do go "behind-the-scenes" to see some marine mammal tanks with dolphins and belugas).
The Texas MedClinic Leon Creek Half Marathon is held on the Leon Creek Greenway in west San Antonio, along with some roads to connect the sections of the trail.