Typical SGs always seem nice in theory but in practise I can't get on with them either. The fret access is actually the one thing about them you don't need to worry about, they've got better fret access than any other guitar I've ever found (even my neck-through, contoured ESPs). The real problems they have though are close to countless. No matter where you place the strap buttons and even with the slimmest necks, they dive headstock-first to the floor every chance they get. The neck pickup tone tends to sound far weaker than on any Les Paul, PRS or thick-bodied super-Strat. Traditional Gibson ones do have horrible tuning issues, especially if you're a bit rough with your guitars on stage. The controls are cluttered for anyone with larger hands and the shallow body means you can be pretty limited in terms of extras you want to stick in 'em.
I keep thinking I'll build a Warmoth SG, since they make their bodies slightly thicker which gives you a better weight balance and more room in the control cavity, but every other SG I've tried has been such a lost cause I'm not sure I want to risk the money on a Warmoth which just might solve some of the worse problems SGs have.
Only exception I've found are the Gibson SG Goddess models, if you stick the strap button on the front horn. Those actually seem to at least balance better, but they're so stupidly thin all-round you get a crap tone out of 'em.
If you want Les Paul-ish tone with better fret access, try PRS guitars (or copies of them by brands like Tokai and Vintage if your budget can't stretch to what PRS ask). They are a touch thinner-toned and just a tiny bit brighter than LEs Pauls, but their usual double cutaway design really improves fret access without them having many of the problems SGs have. A Double Cut Les Paul might also be a good option though I don't know of too many good ones being made these days.