Sorry to hear with the lack of mobility, but hopefully you will still be able to have a few great Copenhagen experiences (apart from U2 of course!).
Will start with the 'bad' news. The giants are in forest areas just outside Copenhagen, but they are far apart and not easily accessible by car. The concept is that the Giants are hidden and you go on a treasure hunt to find them.
For a boat tour, I would recommend to go to Nyhavn and take the Grand Tour with Canal Tours Copenhagen (Stromma) https://www.stromma.dk/kobenhavn/sightseeing/sightseeing-med-bad/grand-tour/ If you manage to do it on a sunny day, Nyhavn will also be perfect to sit and people watch and enjoy a beer before/after the boat ride. Would not recommend to eat there though, it is way to expensive compared to the quality of food.
You are rigth in the assumption that Denmark is expensive, it is one of the things I like about going abroad, it is almost always cheaper. The advantage is though, no need to worry about tipping, you should only do that if you get outstanding service, it is not a requirement or expected.
If you want to try something very Danish you should have lunch at Aamanns Etablissement on the border of Osterbro and inner city (small place hence reservation is recommended). They serve the traditional open faced sandwiches, you would usually drink beer and snaps to go with the food. Unless you are very hungry two pieces are enough and you only feel like a very light dinner. It is not cheap, but high quality https://www.aamanns.dk
For good food at a decent price I often use http://madklubben.dk/en/ . I would recommend 'Hanzo' or 'Alabama Social' as they are located by the lakes of Copenhagen, giving you a great view. If you feel like a coctail afterwards, they have 'Bar next door'.
Casual but good burgers can be found at https://www.halifax.dk/ they are located around the city, there is also one in Osterbro. My favorite is Zurich.
Close to the two restaurants by the lakes, you husband will also be able to find a small beer bar called Soernes Ølbar http://soernesoelbar.dk/ nothing fancy, but they know their beer.
If he wants a larger place Taphouse in inner city is a good place to try an extensive amount of different beers (from what I recall +50 tap beers at all times), but it does not have the same atmosphere as the smaller places but there will always be people, no matter what day of the week https://taphouse.dk/
There a a number of Brewpubs in Copenhagen. One is Warpigs located in the old meatpacking district, now turned into restaurant and bar area http://warpigs.dk/ Do not go to Warpigs unless you really like meat and have to say the crowd is 'younger' and a little bit hipster... just as a warning when I read your post ;-)
Another brewpub is Norrebro Bryghus. I have not been for years, but it is one of the first brewpubs I remember (now the micro brewery thing is all over) http://www.noerrebrobryghus.dk/en
Final brewpub recommendation would be BRUS https://toolbeer.dk/locations/ also in Norrebro.
If you are into beer I do recommend a visit to Carlsberg, they did a renovation and upgrade of the tour a few years ago. I have never been overly impressed with the tour, but it might also be me not being a beer person ;-) From what I know none of the smaller indenpendent breweries does tours I am afraid.
If the weather is good you can also go to the lakes in the morning and have breakfast/brunch at either Original Coffee https://originalcoffee.dk/ or Lagkagehuset. It is a good place to sit and watch CPH everyday life (if you are there early I will pass on my bike going to work ;-) )
Another place you can go is Torvehallerne https://torvehallernekbh.dk/ , where you find a variation of stalls of food, drinks, bakeries. It is always buzzing with life. It is located in the city centre and is open until 7pm.
Ok think that was a start ;-) Let me know if there are some things you would like more information about (I have not given that many tourist recommendations) or if I need to suggest a couple of bars more.
Btw. no problem with the taxi to the Arena from Osterbro. Going from the airport, if you can cope on the day, take the metro to Norreport and then a taxi from there, it will save you quite a bit of money.