Can one Directv sd box provide a signal to two tv's??

What RCA Style output do you have on the receiver? An SD box would only have red/white (audio) and Yellow (Video). You cannot connect this to a Component (red/white audio and red, blue, green video) connection on an HD TV but you should be able to find a Composite (3 wire) to HDMI converter on line somewhere. The coax to a splitter to 2 TV's might still be best. You would also need to add an A/B switch if you want to be able to switch back and forth between watching satellite TV and OTA TV.