I'll be dog sitting in Portland this year, and I've never been to this city! Where are some good places I can shop, eat, and play with my fluffy companion?
I've been there a few times, and it seems like the entire city is dog-friendly. Seriously. If I moved there, I'd expect someone to show up at my door and say "Welcome to Portland ... here's a dog to help you fit in." Which would be completely fine with me. (The cat may have a different opinion.)
portland is a very dog-friendly town, so you'll find all sorts of parks (including dog parks), cafes, etc. that you can visit with your fluffy companion. it looks like you enjoy the outdoors (from your pic), and you'll have no problem finding hiking trails, forest walks, etc. all around you once you get here. i know i haven't given you any specifics, but i hope this answers your question at least a little bit.
Portland is super dog friendly, but I really can't think of any bars or restaurants that actually let them inside. The one exception I can think of is Plew's Brews if you happen to go to the St Johns area. (It's a little out of the way, but the bridge and Cathedral Park up there make this part of town a nice place to visit if you have the time.) It's a pretty chill bar that brews their own beer, has decent food, and a very hippy vibe if that's your scene. Since smoking is no longer allowed indoors here, almost every bar and restaurant has outdoor seating, some with heated patios. Dogs are often allowed on the patios, even if it requires walking through the bar or restaurant. Just make sure you get the ok from someone before getting too comfortable. Roadside Attraction in SE has a really nice patio. Lucky Labrador Brew Pub is of course super dog friendly and has locations in SE, NW and N Portland.
Shops wise, we have so many boutique pet stores that will of course allow your animal to sniff around and sample the treats. Non-pet centric stores may allow well-behaved dogs in, especially if it's a toy breed that you can just carry around with you.
There are a ton of great dog parks which are technically the only places you're supposed to have your dog off leash. There's a million hiking trails around Portland where you're supposed to keep your dog on leash so they don't mess with the native flora and fauna, but you see off leash dogs all the time and your chances of getting ticketed are slim to none. My favorite dog parks are Chimney Park, again in the St Johns area, and Normandale Park near Hollywood in NE, primarily because both these parks are fenced so even if your dog isn't perfectly behaved, it can't get too far. Because of this, these parks always seem busy. Mt Tabor also has a really nice dog park that attracts a lot of dogs, but it isn't fully fenced in.
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I don't know if you need a hotel, but the Hotel Monaco Portland is definitely super dog-friendly and a really cute place.