In Reykjavik we ate in a noodle place which I think was Krua Thai. Not massively expensive and choices for 3 vegetarians. Only DH had beer though.
We had a lovely lunch at Reykjavik Rost too, near the old harbour.
We ate in and took packed lunches for other meals.
In terms of trips, the Golden Circle is a must. Walking around Thingvellir, Geysir and Gullfoss is free except for parking if you drive there. There are lots of information boards in English so you can manage without a guide.
We stopped for great ice-cream on a farm between Geysir and Gullfoss.
Kerid Crater has an access charge but is lovely. You can walk around the rim and then around the lake at the bottom.
The Secret Lagoon is cheaper than Blue Lagoon and is a great end to the day. Literally a hot pool surrounded by grass!
If you don't want to rent a car then lots of companies do half or full day trips.
I would love to have done a whale watching boat trip but my family get seasick on a boating lake unfortunately.
We used Tröll for the excursions that we did and they were fab. And also a bit cheaper than other companies.