Welcome to Seattle!!! I moved from California a few years ago, and I love this city since. I hope you will also find Seattle inspiring and attracting.
In terms of recommending rental places, this is how I break it down for you:
"great walkability and close to lots of restaurants, shops, and bars" --
If you like to feel the vibe of downtown, look in downtown Seattle North of Virginia and East of 2nd St, or Belltown north of Bell Street.
If you like more relaxing neighborhood, search in Capital Hill around Boardway or 12th Ave, or Queen Anne around Queen Anne Ave.
"for a large place with a fenced yard and more room" --
For a lake view and walking by the lake, Iook into Greenlake in North Seattle
For local restaurant and cafes, look into Ballard in Northwest Seattle
For a nice, safe and quiet neighborhood you may consider Wedgewood in Northeast Seattle
For a view of the Puget Sound, I will recommend North Delridge in West Seattle.
I hope this is helpful. You can search for rental on Craigslist. To find rentals listed by brokers you can go to my website and search by neighborhood.
Sounds like you have a lot of recommendations for the Seattle area already. If I can add my two cents, the Eastside has a lot of great neighborhoods as well. Although it won't be as busy as Seattle proper, it's great if you're looking for more room. The most walkable areas I would say are Downtown Bellevue, Downtown Kirkland, and Downtown Redmond. These areas are convenient with groceries, restaurants, shops, and bars close by, but the rents in these areas will be higher than more residential areas.
Choosing an Eastside community or any place to live for that matter, would also depend on where you and your husband work. If you're commuting to Seattle, traffic can get pretty congested, so I would suggest staying in Seattle. If you work on the Eastside, living nearby and enjoying some extra space is great. If you have a car, it's still a quick drive to get what you need even if you don't live within walking distance to a commercial area.
As a side note, we do have a few rentals that you may be interested in, but they are in quieter parts of these cities. Let us know if you want more information and we'll be glad to help. Good luck in your search.