Ah, Plano, Texas, my stomping grounds for the last 25 years.
I'm mostly a street&road cyclist but there are some nice trails for new riders.
Arbor Hills is nice, as is Bob Woodruff/Oak Point. The Shady Brook Trail between Midway and the city limits is an absolute hoot, and if you don't mind riding about a block and a half on the streets (from the west end of the Bluebonnet Trail to the YMCA) you can ride all the way there and back from Harrington Park on the trail system.
When you get that road bike, there are organized rides of all kinds. The little back farm roads of northern Collin and Grayson counties are a cycling paradise. I'm hoping the world class cycle touring found on the little back roads of Parker, Hood, Somervell and Bosque counties don't get "discovered" and ruined.