There are numerous streets that are great for biking. I like to explore streets that are near "designated bike routes."
Designated bike route -- Fairview is a designated bike route.
However, I have found that I like biking on Welch Street more than Fairview. On certain days and certain hours of the day, Fairview can be a little too busy for me. My experience on Fairview led me to test out other streets nearby. The biggest concern for me was to find a street that has a light at Shepherd Street so that I can safely get across that busy street. There are stoplights at Welch Street and at Vermont/San Felipe. In my experience, Welch is calmer (less traffic, slower moving cars) than Vermont/San Felipe. I can also easily connect to Welch from my neighborhood -- I bike on Dickey Place, take a right onto Avalon, left onto Persa, and right onto Welch. All of these streets (Dickey, Avalon, Persa, and Welch) are really easy places to bike. Additionally, from Welch I can easily hop back onto the Woodhead bike route to Clay Street to Dunlavy so that I can safely get to the trails in Buffalo Bayou Park (my fav place to enjoy a leisure bike ride).
The image above is of Dickey Place. It's a small street in my neighborhood that connects to Fairview and Avalon. It's one of my favorite neighborhood streets. This is what a typical quiet, neighborhood street looks like. I'm sure you have streets like this in your neighborhood. Tell us about your favorite streets to bike on where you live.