I recommend staying in or near Fredericksburg--expect crowds even during the weekdays. Don't miss the Willow City Loop--check in the Fredericksburg Visitors Center for maps of other country roads.
Dates are a tough call. Basically the wild flowers start blooming near the coast as the weather warms and then reaches all the way to Oklahoma eventually. Since I live in San Antonio--I plant wildflower seeds in October and watch what they do. So far my bluebonnets are doing great as are poppies and about 25 other varieties. Check to see if the Fred Visitors Center has a website with updates on wild flowers in the area.