Time to Punkin Center is just about 1.5-2 hours from my house at Greenway and Cavecreek. From 87 and Shea it is 40 minutes.
The first gas station on 188 just past the rest stop is called Jakes Corner and they don't have premium gas. If you go towards Punkin Center there is one that has 91 octane on the left.
They have been working on the road past the marina, which is past the bridge (if you haven't seen this bridge you should drive to it, go right onto Apache Trail just past the dam and take pictures). It turns into dirt just beyond the dam. The back side is worth seeing. Of couse there is no water coming out of it because the lake is only 30% full but that is still more then any of the other lakes around combined. You can see where the high mark of the lake was by looking for the Green above the brown dirt area. (I sound like a tour guide teacher). Teddy Roosevelt dedicated this bridge back early 1900s.
If you want to continue to the Marina continue past the bridge and dam towards Globe just past the SRP entrance on your left. You come to a "Front Store" (that looks like it use to be a gas station). Stop and tell them you are meeting me there (I won't be there) and ask for a ride down to the dock. A guy with a golf cart will ride you down to the docks from the parking lot. Give him $5 and tell him to watch the cars for you when he comes up and down. The cars will be fine if you choose to do this. My boat is out on J Dock called Fitzus. There are good restrooms there and pop/beer. Also there is a Forest Service Community Center same area as this store that shows the history of the dam etc (educational and good clean restrooms).
You can continue towards Globe about 15 minutes and you come to another gas station with 91 octane and bar/restaurant. Not bad food. On your way there are Indian ruins up to your right that are worth seeing if you want to take a short hike. It is well worth it. Great views up there and all concrete paths. There is some road construction way beyond this point but not sure. It may all be done but soneone at the store or gas stations can tell you for sure. You can go in most of the camping grounds around the lake and use the restrooms. No bodybothers you.
Cops are bad on this road. They hide. Take your fuss busters. If you have those plates that block photo, take them off. The cops don't like them. If you give these cops ****, they will shoot you.
A little story: At the dock few years back some drunks were at the gas docks and a deputy dog cop wanted to give them a ticket for something? They tried to get in there fast bass boat and take off. The deputy dog pulled the shooter and shot 3 holes in this guys engine. Just a thought!
Another suggestion about meeting at the gas station would be to meet at the one just north of shea on 87. There is more room. The one on Shea is fairly small and tight getting in and out if it is busy.
Have fun. That road is a blast; lanes most of the way and you can see well in front and back of you. First time I hit 130 was on this road.