There's no ski resort inside Edinburgh, but there is skiing near it, and it splits cleanly into two different kinds of day out. First, two dry slopes you can reach in under an hour for a taster lesson or a season of practice: Midlothian Snowsports Centre at Hillend, twenty minutes from the city centre, and Polmonthill over in Falkirk. Then there are the five real outdoor resorts that make up the rest of Scotland's ski country: Glenshee, Glencoe Mountain, Cairngorm Mountain, The Lecht and Nevis Range, all two to three hours' drive north. This is my pick of all eight, ordered by how far you'll actually have to travel, with exact prices, drive times and one honest catch for each. If skiing isn't the plan for everyone in your group, our things to do in Edinburgh guide covers the rest of the city, and for more ideas at this kind of distance, see our wider day trips from Edinburgh.
The dry slopes are the honest starting point if you've never skied or want to keep your technique sharp between snow trips. They're artificial, so the weather doesn't matter, and Hillend in particular is a genuine attraction in its own right: the UK's largest dry slope, with an Alpine Coaster and tubing sessions for anyone not skiing. Bearsden, over in Glasgow, is the furthest of the three but the most club-oriented, with a race and freestyle pedigree behind it.
The real mountains are a bigger commitment, and it's worth being straight about that before you plan a trip around one. All five run on natural and machine-made snow through a genuinely variable Scottish winter, roughly December to April, and a poor year can mean a thin, patchy mountain even in the middle of the season. Glenshee and Glencoe Mountain are the closest, around two hours, doable as a long day trip if you leave early. Cairngorm Mountain, The Lecht and Nevis Range push toward three hours each way, and I'd treat those as worth an overnight rather than squeezing them around a five- or six-hour round trip in the car.