Reddit mentions of Ben's 100% DEET Mosquito, Tick and Insect Repellent, 0.5 Ounce Pump

You say you don't intend on any "serious" hikes, but I assume you will be walking around outdoors. When you are outside, there will be mosquitoes, and it won't matter whether you are right outside your hotel or in the Denali Park back country. The number and viciousness of the mosquitoes can vary greatly. Maybe you'll see one flying around now & then, or maybe you'll be besieged by hundreds of them. Certainly, you want to be ready for the latter.

Like /u/BBBalls, I would recommend long sleeves and long pants. Also, wear a hat. And socks. The more of you that is covered up, the less of you will have to be sprayed. Get a head net, and make sure you know how to put it on, and that it works with your hat and shirt. But keep it in your pocket until you need it.

Also, be sure to have spray with DEET. I wouldn't even bother with the 40% sprays. You can get 100% DEET spray in a spray bottle that will fit in your pocket. (Brand doesn't matter; what matter's is that it is 100% DEET.) Again, use this only as necessary; there is no need to spray yourself with poison when the bugs aren't bothering you. When you do use it, be sure to spray around the cuffs of your pants. Also, you want it on your face, but don't spray it in your face; spray it on your fingers, and then rub it on your face, keeping away from your eyes. When you're outside, don't leave the spray bottle in your hotel room; take it with you. Lastly, the spray bottle can get covered with DEET and messy; you might want to keep it in a zip-lock.

If you're mostly covered up, and you have a head net in one pocket, and 100% DEET spray in the other, then you should have an enjoyable vacation, regardless of what the bugs are up to.

EDIT. It can also help to think about how mosquitoes act. They are drawn by exhalations, and they fly relatively slowly. It is harder for a mosquito to get to you when you are moving. The most common mistake I see people make is to be walking, get a mosquito on them, and then stop to swat it. Then lots of others come. If you are walking, and you want to swat at a mosquito, sure, swat it, but DON'T STOP WALKING to do the swatting. Indeed, it can be helpful to walk faster, or jog for a bit. You can outrun a mosquito.

Also, mosquitoes prefer dim light. If you are under a tree and you get a mosquito on you, walk out into the sun.