Almost all grilled fish is fantastic. If you're not a huge fan, I'd recommend trying a nice thick red snapper fillet. Marinate it in a generous amount of olive oil, handful of parsley, sliced garlic and any other herbs you have/like. Only needs about one hour, or you can leave it a little longer. Heat up your grill - HOT! That is the key to success, in my experience. Take out the fish leaving it oily but discarding all the herbs, garlic. Salt it generously and place it on the hot grill. Don't touch it until it is nicely charred and starting to turn opaque on the upside. It won't stick if you don't mess with it. Flip it over to finish it off. Serve it with a piece of lemon. It is so basic and delicious. If you like it you can experiment with other flavors/fishes.
I am secretly not such a fish fan either. It's something about the texture, I think. nonetheless, for reasons of health, culinary diversity and sheer stubbornness I try to cook and eat it often.
You can eat fish for joy of fish, or because it is a great base for flavouring creativity. I find that if you are not such a big fish fan, the way to go is sauces and flavourings. I find steaming intensifies the fishiness (can't do the 'en papillote' thing), but baking, broiling and grilling firm up the texture, and result in a pleasant but not overpowering taste.
Unfortunately I do not have a grill or a 'barbeque', but this should all be transferrable.
For salmon, try a mix of chopped ginger, soy sauce, honey and lime. Asian flavourings are the best way to disguise 'fishiness'.
Pesto! You can do your own version with different herbs and nuts, but jarred kind is also good. Same goes for tapenade, honey and mustard, apricot jam and soy sauce - whatever you have in fridge, actually. Smear generously.
Wrap little white fish fillets in prosciutto.
I really like trout, cooked whole. I find it tender but not mushy, with a subtle taste. It's great with white wine, lemon slices, handfuls of parsley and shopped shallots and garlic, stuffed inside the cavity (and on top, if you're baking it)
Salsa. I do a weekly fish/shellfish dinner with a friend. This week, he chose bland little white fillets of god-knows-what, and despite my great doubts (and whining - I wanted shrimp, dammit!), I was blown away. Although he panfried, this should work in a grill pan.
Mush the following together:
chopped cilantro/coriander/dhania, minced onion, garlic, ginger and one fresh red chile, and a bit of butter.
Grill one side of your fish fillet, and turn over to cook the other side. Lather some of the salsa onto the face-up, grilled side, to melt onto the hot flesh, and then plate the fish that side down, and spread some on the other side. Mmmm....
Grilled fish tacos are usually a hit. You can use tuna or some of the fleshier fishes that the other posters mentioned or go with snapper or some flaky white fish. Drizzle with lime juice and sprinkle on some cumin.
I usually use a grill pan designed for veggies and spray with a non-stick cooking spray(before you put the pan on the grill) Either do not turn it or tune it only once while grilling
Serve on warm soft tortillas with onion, radish, shredded cabbage and chipotle aoili
Different species of fish taste different. Fish that taste like fish are: tuna and salmon. Fish that taste like chicken are: shark, sturgeon, big halibut, swordfish. Fish that are mild are: rock fish (sebastes), striped bass. Fish that have no taste: talipia.
Grilling fish can be difficult because cooked fish flesh often flakes. A fish grilling basket can help with flaking flesh on the grill. Buy grilling, I mean on a charcoal (or gas) grill, often called a Bar-Be-Que.
Try some halibut steaks on the grill. Defrost if necessary, spread a thin layer of flavored mayonaise on the "top" side, grill over med heat for 7 minutes an inch, turn and cook until done (5-7 minutes per inch).
A local favorite is grilled tuna, either yellowtail (often called Ahi) or albacore, then dressed with a chutney/salsa.
Grill a filet of fish (using a fish basket), seasoned with dry "Mexican" style seasonings, then use in tacos. Try a mild tasting fish such as rock cod (sebastes), ling cod, striped bass (rockfish).
The types of fish I recommend don't mean much if they are not available in your area.
What type of tuna did you not like, how was it prepared ?
Interesting comments about dif. types of fish and their flavors. I recently made a ceviche w/ red snapper and my MIL thought it was chicken. So I guess snapper is a good suggestion for a less "fishy" taste. It may be too delicate to be grilled, but I like it baked in parchment w/ veggies and herbs. Sole and sand dabs are mild and very nice pan-fried in some butter and EVOO.
I like most fishes, but have an aversion to swordfish and shark. Minimal flavor and oogy texture for me. Haven't tried skate, but am dying to. Anyone know if skate wing is available in CA and when? I never seem to see it where I shop...
Salmon is good grilled. My wife takes a flat piece of salmon filet, perhaps weighing a pound (enough for two people), and slaps in on a grill. Turn it over. Serve it up. It doesn't get any simpler than that. A little salt is all you need.
Now, obviously more elaborate preparations are possible. You could brush the salmon in olive oil (though it doesn't seem to dry out when my wife cooks it without any such treatment). You might brush it with a flavored liquid -- a bottled Italian dressing or a home brew brushing (olive oil with dill? olive oil and minced garlic and fresh rosemary?). You could serve the grilled salmon with some sauce -- some snail butter, some mayonnaise with tarragon incorporated into it?