If you don’t mind a short drive to the larger towns and villages, The Windmill Inn at Ings is dog friendly, has a great range of beers and the best Lakeland cooked breakfast I’ve ever eaten.
If it’s a slightly livelier base you’re after, Ambleside is hard to beat. Plenty of options, so there’s sure to be some dog friendly.
You mean the Watermill, But yes, great pub with on-site brewery and EXTREMELY dog friendly (all the beers are Dog-themed!)
It's 10 min drive from Bowness too, so worth a trip for lunch, if nothing else.
for Bowness itself, there's a great Waffle/Belgian Chocolate cafe run by a really nice family - called CHOCCOSHOP. They homemake gluten free waffles with various toppings, and they're incredible. And their own recipe Belgian hot chocolate is an absolute treat. They love dogs too.
There's a lovely back-street Italian restaurant which I recommended to
@Smiffy too, Villa Positano.
For Steak Restaurants - Hyltons in Bowness is probably your closest option - not a steak restaurant per se, but serves a multi-tude of different cuisines (fish, steak, in-house smoked meat etc) and is always busy.
MOST of the lakes is dog friendly and anywhere that ISN'T dog friendly probably isn't worth your time anyway

(though there are a few exceptions)
Other recommendations:
Take a drive to Grasmere - one because it's lovely and two BALDRY'S TEA ROOM in the village itself has THE best Lemon Meringue Pie (and other desserts), you'll ever have.
Ambleside is a nice town with some good pubs/tea rooms/restaurants (the aforementioned Doi Inanton being an incredible Thai and Lucy's of Ambleside being a really good "special occasion but not posh" restaurant - the latter being dog friendly too)
If you're looking for picturesque - can't beat Buttermere - the drive there is an errrr adventure, but worth the stress - although it might be packed in June. Lovely easy amble around the lake with some stunning views.
The Bluebird Cafe on Consiton Water is another favourite of ours too - Dog friendly on the patio and on the picnic benches outside IIRC - food is reasonably priced and really nice. (there's also one in Bowness itself, but it's not as big so can be more of a nightmare to get into)