Bobfish,
We have always stayed at Villa Bella which is on the east side of the island and looks directly out over the cliff to a view of the Ocean. They have a pool, they have an on premises bar and serve breakfast every day except Tuesday which is their day to go off island and restoke the supplies. The rooms are nice and clean. The Palapas are really cool if available. There are not all of the creature comforts of say a US hotel or resort. The owners Ashley and Curtis are husband and wife and they are just downright great people, are both from the US which makes it very helpful if you do not speak spanish. They can also recommend and direct you to anything on the island that you want to see or do. Reasonable rates and good location. Check them out on the web.
info@villalabella.com or
villalabella@gmail.com
If you are looking for high end upscale then goto Rolandi's Resort. It is pricy but just like staying in a 4 star US hotel.
You can also stay right at the Marina Villa Vera Puerto Isla Mujeres Marina.
As far as fishing you can contact Capt. Ruben Pena
seahuahuau@hotmail.com. He can get you hooked up with someone. He is a world class captain and mate and owns his own 33' panga for fishing and snorkling trips but can get you hooked up with someone else's boat if you want to fish on a sportfisher as well. The Keen M is also a good choice as Walt suggested.
Have a great trip.
Thanks
Jim