I should also point out that this is almost the house design except that our back door is lower to the ground (we would only need a couple of steps down) and we don't have stairs down to the basement like the one in the picture.

Need pictures of your deck/patio to provide comments/ideas.

We need a picture of your own place so that we can give a better suggestion. And anyway, this one is really nice.

Put here your own house too and we will give our ideas.

I suppose you could simply 'transfer' those inspiration photos to your own deck area ?

Yes we need pictures of your existing garden. One thought would be to have a deck large enough for the BBQ and perhaps a bench or table and then stairs down to the patio. When you are not entertaining or the weather is poor you may just cook and then eat inside so it is nice to have the BBQ close at hand. Then the other idea is to make the carport so nice that when you do have a crowd over you can move the car and use the carport as a pergola. So make the entrance to the carport large and interesting. Perhaps the side of the carport that leads to the patio could have barn doors that can be pushed back for a party but hide the parked car on most days.

Also search 'narrow gardens' on Houzz pictures for ideas for your narrow side yard.

Here at pics from our house. Excuse the mess... It looks a lot better in summer. We would be taking down that big green tent which houses hubby's boat.

Here are some more pics. One of the reasons we want to take down the deck and create a patio is because we believe it will create a bit more space for us

Patio would be nice. I would plant some tall hedges between the patio, your new car port and property line to hide the cars, boats, and other houses. This would help create a softer sense of privacy and enclosure for your new patio.

Amazon, Which house is yours, and which look do you like? I'm confused...

Yes build a carport with as much storage as you can and make the deck smaller to just hold the BBQ and maybe a table. Then the rest patio. I would spend as much as my budget allowed on the carport because it is so much a part of your backyard. You might even be able to put storage under built in seating on a smaller deck. The idea is to hide all of your necessities such as garbage cans, hoses, extra chairs, and even the boat and truck. Again a carport with barn doors that could be moved aside on special occasions to use the carport space for entertaining in your backyard and to hide the truck and boat the rest of the year.

My house is the second set of pics the wood deck.

Okay, then clear everything away and take new photos so I can see what's going on there. It's impossible to give you exact answers if I can't see the structures clearly.