It depends on the amount of opening between the family room and patio and the overall look you are after.

You could also consider porcelain pavers which look like wood. With modern digital printing techniques, you can now get 2' x 2' porcelain pavers which simulate natural wood including the wood grain and other natural feasts shows inherent in wood.

See a couple of pictures below from the range that we have available for example.

Or IPE stained the same color as indoor flooring,

Yes indeed and Ipe looks just great and it is a fantastic wood species for hardness, durability and stability - but it will inevitably turn to a silvery grey over time in sunlight which then won't match the indoor timber floor.

Handy Deck is correct that ipe will turn grey with time if there isn't any Oil applied to it. Ipe is an overall low maintenance product because it's not as labor intensive as other woods.

Always make sure the material you want is the one that you wouldn't mind it's faults whether its heat retention, labor, lifespan, look, feel. Etc.