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If you can find a six pack out of Neah Bay that will stay inside Tatoosh Island (border with the ocean) if the water is rough, that would be a great option. Just don't know if there are any six packs working out of Neah Bay, and you'd probably need to book the full boat to have that flexibility. Best timing would be May - September, primarily for weather.
How old are the kids....neah bay would be best...and not during halibut season.... Westport is hit and miss on the weather since the only way to fish is to cross the bar. Lapush can be really good with fishing right in front in shallow water. But weather can be a factor.
MHWASH,One of my good friends runs a charter out of Neah Bay. He specializes in bottom fishing and runs trips in 4b all year. If I were you I would book one of his shallow water lingcod or 4b rockfish trips. 4A is the ocean out of Neah Bay and 4B is the straits, fishing in the straits you typically can have better weather and currently the fishing is phenomenal and is open all year although its currently only open for black rockfish. His bottom fish trips on the ocean run from April - whenever lingcod closes but the shallow water trips the runs are short and fishing is hot, if you go when deepwater lingcod is open there is a spot that is close yet awesome and is by far my favorite spot to fish lingcod. Neah Bay may be a longer drive but has benefits. 1. There is no bar to cross. 2. The straits are protected and fishing is great. 3. Tom's boat is a 6-pac boat so your experience is different. 4. He is used to taking kids, if the weather cooperates we will take a 3 and 5 year old out this weekend. 5. He is an awesome captain, about 80% of his customers are returning customers, that says a lot. 6. He likes taking 3-5 people if your booking as a group of 4 you can have the whole boat to your group. Either way, that's my plug. I'm sure others on this site have had great experiences with him.Here are his two websites he runs the boat, his wife runs the inn. I believe there is a discount if you get a room and a trip. http://excelfishingcharters.com/http://www.theinnatneahbay.com/