1
We can meet at 2 p.m. or eventually at 3 p.m., whichever is better for you.
We can meet at 2 p.m. or possibly at 3 p.m., whichever is better for you.
Eventually does not mean ‘possibly’. Use possibly or perhaps when you are suggesting another option.
Eventually means ‘in the end’, often after some time or difficulty: ‘We searched for the keys and eventually found them in the car.’
2
First, the hotel was clean. Second, it was near the beach. Eventually, it was cheap.
First, the hotel was clean. Second, it was near the beach. Finally, it was cheap.
Use finally, not eventually, to introduce the last point in a list.
See END (2)