Towing to Crater Lake Oregon

Didn't say when you plan on going but watch the NPS site for updated info. https://www.nps.gov/crla/index.htm

Do the lake loop drive or take a trolley. They make several stops. I have taken our 35' around the lake twice, the road is narrow and rough in some places but totally doable.

Walk around the Lodge for some nice views. The food at the lodge and the snack bar is $$$ but decent. There is a restaurant down near the South entrance which was reasonably priced two years ago.

Stop at the logging museum at Collier St Park. The campground is closed due to fire damage but the museum is limited open. It too had fire damage. https://stateparks.oregon.gov/index.cfm?do=park.profile&parkId=165

"Any issues up to Crater Lake I should worry about?"

Beautiful drive. Should be lots of frozen water to refill your tank.

Only worry is snow, lots of it! 11 feet average.

We were there in early June 2019 and the road around Crater Lake wasn't open yet. But the main roads were great. If you've never been there it's a beautiful area

Highway 97 is fine. Highway 138 to Crater is straight as an arrow and climbs to 5,900 ft. It is way too early to say there are no issues. I've been snowed on at nearby Diamond lake (5,200 ft.) in early June.

the road is fine all the trucks coming from the south land to central oregon use it,
if you haven't done so start hunting for reservations crater lake is area is very popular

Nope.