My suggestions:
23 Oct Bilbao sightseeing including Guggenheim museum in the evening - what not to miss? local non touristy food reco?
In the old town, don´t miss the Ribera market, best in the morning (most stalls close at 2pm) church of San Antón (the oldest building in Bilbao), the 1397 cathedral of Santiago and its square, Plaza Nueva…
Going up by Gran Vía (main) street you´ll find Diputación street, there´s a statue of John Adams with some of his kind words on the Basques, after his visit here in 1780 with his sons John Quincy and Richard. Right there, El Globo bar offers very good pintxos and La Viña del Ensanche has a great menu, for foodies and not expensive.
Funicular of Artxanda, one every 10min, once on top go left for great views from the balcony overlooking the city, right for Restaurante Txakoli, wonderful views and great menu, anything will be excellent and rightly priced.
ZUBIZURI bridge, how a beautiful bridge was such a big fail in architecture (Google for more info...), and Isozaki Towers, depending on where you look at them it seems they enter or they exit the river...
And don´t miss Azkuna Zentroa, a former wine warehouse transformed into a civic centre by French designer Philippe Starck, don´t miss the columns (all very peculiar, showing all architectural styles) and the transparent swimming pool!! Also, a rooftop bar with great views for excellent cocktails.
You may like to visit the Puente Colgante (aka Puente Bizkaia), the unique transporter bridge, a UNESCO World Heritage Monument, accessible on our safe, clean, modern and cheap subway system. Something unique in the world. Also, beaches nearby, if you have the time it´s a beautiful promenade right of the bridge until you reach the Puerto Viejo of Algorta, quaintest little place with bars and restaurants, locals only.
Lunch is our main meal of the day, not dinner, so I´d recommend to enjoy the affordable daily menu, offered at many restaurants in the old town and in other parts of the city, for around 20eur including half a bottle of wine per person.
24 Oct San Juan de Gaztelugatxe and nearby villages - tips for best photography spots and places to stop nearby
Bermeo, Mundaka, Elantxobe, Ea and Lekeitio are must-sees, as well as the beaches of Laga and Laida near Ibarrangelua. There´s the Urdaibai Bird Center, if you like to take pictures of the birds at this Reserve of the Biosphere. Ereño is a very nice town on the way to Lekeitio.