West End is more a backpacking, serious divers vibe. I would definitely not call it a party atmosphere considering there are pretty much two bars in the whole town. West Bay is a nice beach but VERY touristy and gets absolutely packed on cruise ship days. They are about 10 minutes from each other on a water taxi and 30 minute walk down the beach.
It might be below your standards but I have been there with my family multiple time and our favorite place to stay is at the "Mi Casa" rental house and then dive with West End Divers. They are right near each other. There is a great restaurant on top of West End divers, called cafe esconditio, where you can get breakfast and lunch (or you have the freedom to go elsewhere). The kicker, the rental house is between $300-600 a week depending on if the owner is running a special. That leaves a lot of money to enjoy other things on the island. I would not recommend Splash inn. There is nothing wrong with it, it was clean but it is a bed in a room. Nothing special at all and the rooms are directly above the bar so we were listening to terrible karaoke all night.
If you want the pool, beach, diving in a more secluded area look up Turtle Beach Roatan. It is about halfway between West Bay and West End and the dive owner/master is great! Her name is Denisse and I used to dive with her at another shop before she opened her own. Most places in West Bay are nicer, I would probably recommend Infinity (for more resort like living) or West Bay Lodge for a more local but still very nice place.
In terms of weather, keep your eye on it but in Oct 2013 I was there for a week with no problems at all and Oct 2014 I was there for 2 weeks no problems. So yes it is technically the beginning of rainy season, but that is in no way guaranteed.
And Roatan it is entirely possible to get out around $2K. Last time I was there: $50 to/from the airport, $300 for the week MiCasa rental house, $35 per dive with West End divers (equipment included), Breakfast approx $5 per person/per day, lunch $1.50 for a Baleada up to $10 for a large meal, dinners are about $10-15 per person per day.
I would also recommend looking at Utila for your budget. Same concept as Roatan but a couple nicer resorts that are less expensive.