Question
do you know any hearty ground cover I can get that will spread quickly, look pretty and grow in the sun.  I am looking for one?

Answer
You left out low-maintenance -- oversight, yes?  Low maintenance is the order du jour.

Alchemilla Mollis.  Campanula Portenschlagianal.  Sagina subulata.  There are SCORES of hearty, hardy, sun-loving groundcovers with and without flowers.  Click on 'custom search' at the Bluestone Perennials menu, then plug in the numbers: www.bluestoneperennials.com.

There are others.  I can tell you that any number of sweet, delicious Strawberries will spread all over the place thanks to their runners in every direction.  The leaves are attractive and if you play your cards right you don't need to spray or defend against slugs or bugs.  Every spring, a crop of fresh, sweet, delicious Strawberries for breakfast; between seasons, a beautiful, thick carpet of those serrated leaves:

http://www.gardenguides.com/how-to/tipstechniques/fruitnuts/strawberries.asp

If you're a Rose lover, you might consider low growing Roses made as a groundcover.  This is not my cup of tea but it might be what you're looking for.  Let me know if you'd like more on this.  Amber Cover, Innocencia Vigorosa, and the nearly thornless Taos:

http://www.helpmefind.com/rose/pl.php?n=35697

http://www.helpmefind.com/rose/pl.php?n=50654

http://www.helpmefind.com/rose/pl.php?n=45354

Viola odorata and other spring Violets have a reputation as shade plants.  In truth, Violets actually do not do well in Shade.  With a full sun exposure, they bloom and multiply much more happily.  They are not however what you would call 'invasive' and do not spread aggressively.  Their fragrance may have you rethinking your conditions.

Speaking of fragrance, if you live in Zone 7 or warmer, consider the more recent hardy compact Gardenia selections.  One called 'Fragrant Pathways' is one of the most compact hardy Gardenias on the market, with a strong Gardenia fragrance and spreading habit.  It's under 1 foot at maturity and blooms all Summer before going dormant.

Thyme 'Ruby Glow', another fragrant groundcover, spreads quickly and endures drought and poor soil.  This particular hybrid has a deep pink flower.  It blooms in late spring/early summer.

Delosperma -- 'Hardy Ice Plant' -- is not commonly grown, at least where I live, but I do have it tucked away, test driving it for future use if needed.  This is a short, low maintenance groundcover that has never wilted when not watered, spreads nicely and blooms  sporadically for me.  Some varieties grow faster than others, but as succulents they will never ben demanding.

Candytuft, Snow-in-Summer, and Alyssum Saxatile Basket-of-Gold are Spring blooming groundcovers that put on their best shows as Spring Bulbs put on their show.  The blooms are intensely white or yellow.  Although they need care to be healthy enough to spread for the first few seasons, they are so brilliant I had to include them.

Finally, the popular Sky Blues of Plumbago are barely a half foot in height, but spread aggressively.  Evergreen and drought-tolerant, P. auriculata's 'Royal Cape' hybrid has large, blue flowers that begins flowering in late spring and continue through the season.  Ditto, Phlox subulata, the late spring favorite with fragrant blooms in pink, violet or white, a favorite for sloped landscaping.

I suppose Grass is out of the question? Fits all your specs.  Bentgrass (crewcut-height putting-green grass) fills spaces between stepping stones nicely.  Of course you have to mow it every other day.

These are the prettiest I know, none require mowing.  Good luck picking one.