Welcome to our fair (wet) city! The advantage of visiting right now is Alexandra will get a good sense of the winter/early spring weather. Summer and early autumn can be idyllic (and therefore a little misleading). It's supposed to get sun-breaks then sunny into the week, although I don't know how long you are here for.
I don't own rain boots - sneakers and boots that are okay with a few splashes are fine and I only carry an umbrella if it's pouring, although usually you just wait three minutes and a squall passes and you can walk just getting dripped on. I usually wear trench coats on rainy days, but gear raincoats are popular.
Will you have a car? Portland's public transit is good (look at Max and street car routes around downtown), but if you want to look at the vibrant/hip young people neighborhoods that might be helpful, although you can bus there too. Things that are relatively close to where you are staying are:
-Portland Saturday Market - a weekend craft and random handmade things market, but also has food carts -- there are also good food carts closer to the downtown library in a courtyard - food carts are big here, and very tasty/diverse -- some restaurateurs move to town, open a food cart to gain a following, and then move into permanent digs.
-Portland Chinese Garden - some of our trees are blooming now, and the tour and tea house inside are worthwhile.
-Powells city of books - my one must see. Prepare to lose hours if you like browsing.
-the Arboretum - if you want to see big trees or take a short walk to look over the city and see the surrounding white-capped volcanos.
-At night - Portland has a lot of restored old theaters that show second run (and some new movies) for much less than the chains and sell good beer and pizza. Most neighborhoods have one fairly close by (Bagdad, Laurelhurst, Academy, Hollywood (for indy films), Saint Johns theatres are all good times)
Neighborhoods that are worth walking and eating at to get a sense of what Portland is about:
-North Mississippi Ave. - great food carts and cafes, some clothing boutiques, the rebuilding center (which has very cool architecture made out of reclaimed stuff). hipster (Also N Williams which is close).
-NE Alberta Ave. good cafes for breakfast in particular, some clothing boutiques, some galleries, a little cluster of fabric/yarn stores. hipster
-SE Hawthorne Ave. - one of the older alternative neighborhoods (hippie rather than hipster). Food, fair trade boutiques, a cluster of young peoples' trendy resale shops - Red Light Clothing Exchange, Buffalo Exchange, Crossroads, and a curated Goodwill. (Also SE Clinton Street and SE Division if you want to go further south)
- Or closer to downtown, on your side of the river -- NW 23rd Ave. trendy, too wealthy for hipsters, but has various good places to eat and lots of boutiques.
Then a caveat about moving here. Portland has been gentrifying quickly. Rents have gone up in all the closer in neighborhoods dramatically in the last 5-10 years. A lot of young people who move into town are now only able to afford the further outskirts or suburbs which can be pretty charmless, or have more of a strip-mall ambiance although they are changing too. The job market is not great without specialized skills. If Alexandra is into the outdoors, alternative lifestyles/progressive politics, biking, gardening, craft, microbrews or wines, or great inexpensive food -- it's good for all of that though.
PM me if you want more info or to have someone to text with questions while you are out and about, I'd be happy to help. I'm working at home this weekend.
ETA: oh, and for what's on in town the free indy papers the Willamette Weekly http://www.wweek.com/homepage/ and the Portland Mercury usually have good listings.
ETA2: there are some particularly dog-friendly cafes in town if you want to give Baxter special treats. Two that come to mind with covered patios/dining with your dogs and dog dishes on the menu are the Tin Shed: http://tinshedgardencafe.com/ and a brew pub: the Lucky Labrador, two locations: http://luckylab.com/
