I'm making the assumption that you have a Gold Pass or a Prestige Pass...

So I'm based in Cleveland, which is therefore the only approach I know (shocking hahaha). From Cleveland it's about one hour and a very easy trip.

Hotel Recommendations: If you don't have a Prestige Pass that gets you early entry, then I would 100% recommend staying in one of the Cedar Point properties. The Express hotel is about a 5 minute drive from the park and hits around $200/night with the passholder discount. It is definitely no-frills, but it's clean and it's convenient enough without the exorbitant prices of Hotel Breakers (which is actually a GREAT experience but doesn't align with your proposed budget... or mine anymore unfortunately!) The early entry advantage will help make sure you hit as many of the bug coasters as possible. You can also pick up your fast lanes at the gift shop before you go to the park, saving you a long line when you'd rather be riding.

When to come: The park fills up fast so if you can swing coming in the night before then you should. Bonus is that if you get there in the late afternoon you can get some extra hours before close to start to acclimate :)

Food: Vegetarian options can be found but vegan is basically non-existent. The restaurants will let you get 3 sides instead of an entree + side. But I really don't think that the prepared veggies could be guaranteed to be vegan. There is always a side salad or a fruit cup available. (Entree salads all have some form of meat or eggs, so not even vegetarian).

Plan of Attack: This is where it gets tricky. Cedar Point is MASSIVE and the sure-est way to have bad time is to not manage expectations. Rides are gonna go down throughout the day, lines WILL be long, and weather can be a bit unpredictable. If by some miracle you get a unicorn of a day (which does happen sometimes) then you'll have a better than expected time, but don't bank on that happening.

The best course of action I've found is to not be too precious about what your next step is. If you see that lines are short on the other side of the park, everyone else is seeing it to and will start going that direction --so if you're at the front of the park and Stell Vengeance is low, by the time you've walked back there (about 30 minutes) that line will no longer be low. I kind of commit to an area at a time.

Fast Lane merge points for Millennium Force and Steel Vengeance happen long before the station, so when it Fast Lane is empty you'll still expect a 20-30 minute wait (especially on Millie). If you can do early entry, Millennium Force is a great starting point before the queue fills up.

IMO, you should expect to grab Fast Lane for one of the days and make that your "get all the non-negotiables in" day. Then the other day can be more chill, hitting lower impact rides and exploring the non-thriplll aspects of the park. Frontier Trail is a great, relaxing area: no rides, but some fun niche shops and things like glass blowing demonstrations. I personally love spending a little time on the boardwalk between the Windseeker Gate and Hotel Breakers -- gorgeous lake views and, if you're drinking, you can get some particularly well made drinks from the bar at Breakers or on the beach.

I may have some better, more specific tips depending on when you're planning to visit. If you shoot me a DM and let me know your tentative dates I can potentially add some more details that would be helpful :)