My favourite rides usually involve the B road through the Moorfoots to Innerleithen.
Traditionally, I do my first ride up the Granites on the morning of Paris-Roubaix. Often gets the added bonus of loads of mating toads and hungry herons at Heriot Water if the weather's good. Not long to wait now.
Back OT, favourite rides from Edinburgh by category are:
Flat and fast (when there isn't a strong westerly) - East Lothian via Musselburgh, Prestonpans, loop on the back roads from Aberlady to West Fenton etc, back by Gullane. I'd advise avoiding the inland mainroad of A198 and B1377 which tends to feature impatient and or fast driving.
Long climbs - The Granites via Middleton. Depending where you turn back on the B7007 between Middleton and Innerleithen you can do one, two, three or four long "easy" climbs, or you can throw in a nasty one by going over Soutra if you're happy to do a mile or so on the A7.
Nippy steeper climbs - Bathgate Alps: any combination of the lanes in the rectangle between Winchburgh, Broxburn, Linlithgow and Bathgate.
Epic climbs - the Lammermuirs from Gifford to Duns.