Public transport in Copenhagen was good, and for families it has an extra bonus: for one paying adult two children can travel for free. Also, there are several affordable bike rental places also for families with toddlers, as they have many bikes with a big “basket” in the front that fits two or more kids. It seemed to me CPH would have been an easy city to ride a pushbike in but with an unstable weather we ended up doing other things.
In my opinion omenahotels.com is a great budget hotel option for families as you can book 1-4 people in the same room for the same price. Rooms have a double bed and two pull-out sofas, and as they are for 4 people they are usually big enough to fit strollers inside too. Rooms also have a table, fridge and micro, which I find practical with small children; no need to eat every meal and snack out.
Downsides of the hotel would be that there are not many (or any) shelves or closets, the rooms are cleaned only every 5th day (comes with the price but after 4 nights there with kids I really wished there would have been at least a brush and a shovel) and our bathroom could have done with a facelift, But hey, it is a budget hotel.
Omenahotels are always situated close to the city centre, which is great but in Copenhagen it seemed that this side of the train station had its fair share of seedier shops. This did not concern us, but may be a down turn for some. We have tried Omenahotels in Stockholm and in several Finnish cities, and they have usually been worth the money (only in Vaasa and the bathroom in CPH have left something to wish for ). Oh, and this is not a paid ad :).