Max temp depends on your animals. Some fish and corals are barely tropical, and will get stressed at 80F. Some are just getting comfortable at that temp and are happy up to 86F. Many snails available in So Cal are collected in Baja and are not really tropical snails, so they do very poorly at hot reef temps, and when temps spike... they cook.
It's more important that you keep the tank temp steady. A couple of degress of swing is fine and normal in the wild -- going from 77-78F and spiking up to 84-85F will cause some damage!
Without a chiller you need fans, fans, fans and good ventilation. Get the hot air from your lights blown away from your tank (fans in the canopy and stand). Get air blown over the water to encourage cooling by evaporation (fan over the sump.) Keep the water aerated with vigorous overflows and good skimming, which will also help evaporation.
Keeping my stand doors open and canopy doors open in the evening does a LOT to bring the temp under control on hot days. This is just ventilation; basically the hot air doesn't stay inside the stand and heat the water more.
Emergency cooling: water change with cooler water, frozen 2-liter bottles in the sump, turn off the lights and extra pumps (like the skimmer).
Here in So Cal it gets cool every night, so as soon as the temp outside drops under 80F, get the windows and doors open on the shady sides of the house and start up fans in the windows/doors. When the sun goes down you can open up the west side of the house, too. A big box fan in my door, with the back door and windor open, will blow (or suck) air right through my house and ool it off.
Don't forget good blinds or curtains, even if you have good quality windows, insulating drapes/blinds will cool the house by several degrees on hot days.