My son has ASD and this is something we've had trouble with too. I can tell you what works for DS, every child is different so it might not work for your son but it's worth a go.
Social stories. You can make your own (there are guides and examples online) or some venues have them on their website for download. It shows where you're going, what it looks like, what you might see/hear, etc. and helps with anxiety about the unknown. We read the story before going to prepare.
Plenty of warning for transitions. A digital watch was good for this as I could set alarms for him alongside my verbal reminders. For example, leaving the park "Ten minutes and we're going to leave.... Five minutes .... Okay, last turn and then time to go ... Right, home time."
Telling him in advance where we are going and why, how long we'll be there, and what he can do if he's had enough. Having a plan helps him. So I'll say "we're going to Tesco. I need bread, milk, and something for dinner. It'll take around half an hour. If it's too noisy or busy for you, you can have your music on" (he has headphones and an iPod).
Headphone. Or ear defenders. They cut down on the amount of sensory input coming in. Ditto an iPad or handheld gaming toy. Anything he can use to shut the world out a little and don't worry about anyone judging you for using it, that's their issue not yours. One afternoon at the park in the summer DS was sat underneath our picnic table with his headphones on, a towel over his head, playing on his iPad because he needed to shut out the world for a bit.
Give him outlets. Before he was diagnosed we used to get really self-conscious about him stimming, twirling, clicking, etc and would try stop him. Now (so long as he's not harming anyone or causing a danger) we let him, mainly because we now understand more about his condition and we know it serves a purpose. We also have a kit for him that helps meet various needs - chew toy, fiddle toys, etc.
We also try and avoid situations we know he doesn't like or we manage them to fit. For example he loves softplay but hates crowds so we go when we know it's going to be quiet (midweek after school, sunny days, last session on a Sunday). He also loves the walking trail at our local National Trust so we go when it's raining or cold. We go on holiday during off-peak and in term time. We look for ASD-friendly sessions at local attractions a d we have a CEA card which gives a free carer ticket for the cinema and a Max Card which gives discounted/free entry (and often queue jumpers) to loads of attractions to help mitigate our costs if he wants to leave early or can't/won't access all the facilities - you don't feel as bad about leaving the ££££ attraction after only ten minutes if you got in for free and didn't have to queue!
Are you a member of any ASD support groups locally? I'd recommend doing a Google search to see what's available, they often do clubs and events specifically tailored towards children with ASD as well as education courses and workshops. I take DS to clubs and events through ours and it's nice to be amongst people who understand, no one bats an eyelid if he has a meltdown (they offer to help!) and no one thinks he's weird or rude if he doesn't join in or if he plays differently to the other kids.