Nami is the hardest of the 3 girls to marry, mostly because she goes wherever she wants whenever she wants and she only likes a few items. Unlike Celia and Muffy, with Nami the fastest method of marrying her is to get her to 3 red hearts and then end the chapter, so that the game will get Nami to ask you if she can move in with you. The points needed for red hearts with Nami are as follow: 1 red heart = 9 points 2 red hearts = 13 points 3 red hearts = 21 points
There are 3 different ways to increase your points with Nami, giving her gifts, heart events, and talking to her. Giving her a gift and heart events give you 1 point. Talking to her may also give her 1 point (it may only be 0.5 point), but is very random and rarely ever works. To try and get the point for talking to her, you need to talk to her in her room, which you can only enter at either 7:00am or 9:00am, if she hasn't already left. The only gifts you can give her are statues and fossils from the ruins, and Trick Blue Flowers which only grow in fall.
Because the fastest way to marry Nami is by ending the chapter with her on 3 red hearts, it's faster to sleep until Fall and give her 20 Trick Blue Flowers. If you're doing this in a no-reset/marathon situation then you may want to go to the ruins in the last few days of Summer and give her some statues and fossils. Because you need to get 21 points in order to marry Nami, you need to give her a gift everyday from Fall 1 until the end of the year, but you also need to activate a heart event. There is only 1 heart event that appears in the run, which happens a few days after you get 1 red heart. In this event there is only 1 option box and the correct choice is the second one.
In this run you will also want to get a horse in order to save a lot of time. To get a horse you need to ship/buy something any day from Spring 10 onward, so that the next day at 12:00pm Takakura will bring you a horse. Any time after 1:00 and you will not get the horse, so you don't have a lot of room for error. Luckily the only thing you'll need to do in Spring/Summer is milk your cow twice, sell it and then sleep until fall. If you ship some milk on Summer 10, you can get the horse on the day you start befriending Nami.
Nami's will go wherever she wants, but the best bet is usually Romana's mansion. I recommend going to Romana's mansion first, then checking the area by the beach, then by Celia's farm. Sometimes Nami will leave the valley and go to town. On these days you can't give her any items.
That covers everything for Nami. Time saves are mostly the same as ones in Celia and Muffy runs, but the biggest time saver is just being lucky.