In reply to Mike-W-99:
That's mainly the climbs in and around the South Quarry, though, isn't it? (Maybe plus the columnar basalt Camson's Ribs, which are a tad close to the road. I don't have my copy to hand to check for sure.)
The OP seems to be interested specifically in gaining the summit, which the top of the South Quarry ain't. That said, it can be a satisfying place for a donder, and some of the routes could pass for short scrambles. (I believe that in theory you don't need a permit if you're not doing roped climbing. But the park rangers may take a different view. AIUI there's no "right to roam" in Holyrood Park - it's all permissive, so basically their word is law.)
There's the Cat Nick, but reports I've read suggest that it is somewhat loose, and the park rangers can be picky about it because of the risk of stuff being dislodged on to people walking on the Radical Road below. At the north end of the Radical Row is someone-or-other's (Harrison's?) Pinnacle but I think that may risk attracting attention from the security bods at the Scottish Parliament if you aren't careful.