The Bagel Cafe on Mason Rd. @ Kingsland in Katy is a terrific spot for fresh bagels, including an awesome "French Toast" bagel and three varieties of cheese bagels (swiss, cheddar, and asagio) that make delicious sandwiches. They have muffins, strong coffee, and lunch fare as well.
Only a placeholder web site as of now, so no menu to see... but trust me -- stop by the store anyway.
Tip: they're not open on Sundays, except for private functions.