Damn, I want to do this trip.Just scanning this thread you've had some good recommendations already but drop me a pm and I can e-mail you a load of other options.
I'm from about an hours drive North of Edinburgh but live 'doon Sooth'....still get home a couple of times a year though so still in touch with where to go and what to see.
4 days simply won't be enough,try to squeeze a week or 10 days out of it and you can afford to take a trip into the Highlands and if possible as far as Skye and Applecross.I cannot recommend highly enough a trip through Perthshire & The Trossachs.I lived in the Rannoch area for a while and can recommend any number of places to stay and visit.Ideally hire a car and drive the A82,you will discover the correct usage of the word awesome as it carves through Glencoe(you may have gotten a glimpse of this if you watched Skyfall)I'd also recommend Pitlochry and Aberfeldy. Beautiful area and some very good distillery tours(Edradour,Blair Atholl and best of the lot IMO Dewar's World of Whisky at Aberfeldy...you can also raft down the rapids on the river Tay which will be a blast in March!!)
3 or 4 days in the Highlands still leaves you a long weekend in the city.
First off Edinburgh is in my biased view one of the most beautiful cities on earth.it's small enough to wander around but big enough to be a capital city and has that big town vibrancy(Ok if you're from NY everything else seems small but trust me )you won't be short of things to do.The Castle is an absolute must see.It's hard to describe that moment when you are driving through central Edinburgh when the castle first comes into view..properly awesome...you'll know exactly what I mean when you experience it.If you are there in March you might be able to see a 6 Nations Rugby Interntional.It's worth trying to coincide with a game as the atmosphere in town on rugby weekends is like nothing else.Tickets can be hard to come by as the tournament is so popular but I have some rugby contacts so let me know.
Everyone talks about he deep-fried mars bars and haggis and yes that's worth trying for novelty value but Edinburgh also has some great restaurants and you can eat at Michelin star standard in a number of places,definitely worth treating the old girl to dinner at Tom Kitchin's place or Martin Wishart.Take a stroll down Leith way.It used to be 'mingin' but is now upmarket and full of trendy bars,cafes and restaurants(remember the word 'mingin' you'll hear it a lot especially in and around the pub!!).
If you really want to treat the lady then a night at The Witchery is worth spending a bit extra on.It's an atmospheric and very highly regarded hotel yards from the castle esplanade with a top,top restaurant.Great if you want your romantic credentials to go sky high although the credit card may feel the pain for a few months!!
There's basically too much to do,you'll love it especially if you don't care too much about he weather.As I said pm me and I can I've you as much help as you need.Here's a great book I recommend to anyone visiting Scotland...you should find it on Amazon no problem.The guy knows his stuff and is spot on with his recommendations....enjoy