So I wanna take my boyfriend on an outing it's not like I don't enjoy cuddling on the couch and watching movies or playing video games it's just I wanna go out somewhere where we both will have fun...the only thing I've come up with to do is late night arcades, going to the movies or both. He dislikes going out in the sun so that's why I don't have any day time options.
My main questions here are:
1. Roughly how much should money should you take to an arcade without it being too expensive but you both can have fun
2. What other places could we go to instead of an arcade?
Well that's about it...so thanks for taking your time to read this..

Sounds like someone needs a trek outside of their technological safe-zones. What needs to happen is a day without all that stuff so that you can expand or broaden your horizons so that you feel a connection regardless of where you are or what you're doing.
I'd test the waters a little- that's all I'm saying, but bring a cross and some garlic in case his fear of the sun is a bit more than I anticipate.
A perfect date is limited to how much money you spend- hell you should be able to have fun together on a hill with a worn blanket and a starry sky~ Go wherever! Make an adventure out of it. Just so long as you have each other, it should last.

1. My girlfriend and I can go to arcades and enjoy it for about $10, and that is split between the two of us. We are in Japan right now, so most games are about a buck each, but we make it last.
2. If he insists on going out at night, maybe go out to dinner? Try researching some cheap local restaurants, and grab dinner before the arcade. Also maybe frozen yogurt? Those places tend to be open pretty late. A comic book store maybe worth a shot as well.

>>2 I lolled at the cross and garlic thing :DDD

TBH tho, Unless he's an ass, you can convince him to go out at daytime relatively easy, just think of reasons why daytime is better than nighttime for a thing that you want to do. I.e. If you want to take a walk or sth at midday at a beach idk.. Tell him that you want him to feel the sun, "warmth of the sun is amazing" when you're out tell him to try and focus on the suns warmth for a minute, make sure to smile and make him smile (:

Personally I also prefer nighttime as it's more peaceful, romantic and it makes you feel more free.
one of the many things you could do is just go somewhere with trees and/or water and sit/lay on a blanket and just play some card or tabletop games whilst looking at the starry night sky (: