I emigrated to northern Sweden in 2019, but in fact my very first "landfall" in the country was when I flew to Gothenburg and caught the SJ night train to Umeå for an interview. I had a lovely few hours exploring the city on foot, wondering if I could live in Scandinavia.
Others know the city better than I do, but some general thoughts regarding costs...
Yes, Sweden will feel expensive. It's the same for us, and in general Sweden is a home-oriented society. I work in a university and even in normal times, students simply don't go out to socialise very much. Parties etc in the home are more common.
A few adjustments to your travel routines can help. Try not to stop and snack while you're out and about... two coffees and pastry in a café will set you back a tenner immediately. Others have mentioned
Systembolaget, which is the state alcohol monopoly for off-sales. If you want to drink at home you can only buy 3.5%< beer, wine or spirits there. Larger stores are open 10-20 on weekdays. They all close at 15 on Saturday and don't re-open until Monday morning.
Drinking out, the cheapest pubs don't always look like "pubs" to British visitors. The best pub I found in Stockholm actually presents itself as a Japanese restaurant... but go inside and it's a rather cosy bar which serves 100x as many beers as it does bowls of noodles. So if you want a drink at the end of a long day of sightseeing, consider a restaurant or diner - those with licenses are often fine with you sitting in to drink.
Most hotels include breakfast, and even in Corona-times to breakfast buffets at Scandic hotels are wonderful... so fill your boots every morning.
(Not literally... they don't like it if you take out...)
For lunch, most Swedes eat between 12 and 13. The way to get good value here is to find somewhere with extras thrown in. Many places will offer an inclusive lunch ("
lunchmeny") with bread, salad, and coffee. Grab the daily newspaper in the hotel, which may have a "
lunchguiden" with small ads for today's specials Look to pay 75-120kr for something like this. Ikea canteens have been closed for much of the pandemic, but the one in Gothenburg may be open if you make it there. Most malls have food courts with slightly cheaper deals. Department stores like Åhléns (mid-range, like John Lewis) and NK (high-end, like Selfridges) also have eateries.
For fast food,
Sybilla is cheap and not so nice (and they always seem to be located in bus stations...)
Max is Sweden's McDonalds, and unmissable. Almost everything can be made vegan or veggie, just swap the patty for one of several plant-based alternatives. Pressbyran (newsagent), Seven 11 and Circle K (gas station) all sell cheap hot dogs which you can have in a variety of flavours and breads.
Others have given you advice on paper of PDF tickets for the airport bus and local transit. But in general, almost all transport ticketing in Sweden is now handled on mobile devices. Search your iOS or Google app store for the name of the operator. Some operators make this difficult for visitors by a) not listing their app to users with app store accounts registered outside Sweden, b) not accepting payment from non-Swedish debit cards. You will also encounter a lot of vendors who offer "Swish" - this is a widespread mobile payment system only available to Swedish residents. But in general, buying online or in an app and then scanning a QR code is how it works. Under current circumstances, some Swedish transport operators (such as SL ferries in Stockholm) are not checking tickets in order to reduce the risk of exposing staff to infection. But interpret that opportunity very carefully.
Again, I don't know about Gothenburg, but in general the current procedure is not to board at the front of the bus. If you have to scan your ticket there (often in rural areas) do so when the front door opens and then board at the middle door.
Finally, Sweden has taken an approach to coronavirus which believes that total usage of face masks is less practical and more wasteful (i.e. drawing essential PPE supplies away from healthcare) than simple social distancing. There are no rules on you as an individual, simply a strong recommendation to stay home if you feel ill, avoid unnecessary use of public transport and to maintain 1,5 metres social distancing. Some shops ask for 2 metres. Personally, I have found it very difficult to maintain those distances in busy public spaces, especially supermarkets, so I have re-useable cotton face masks that I use indoors in public and wash daily. I would encourage you to do the same if you feel safer doing so - do not let the attitude of others affect you. No-one has given me hassle for wearing a mask, there is no "anti-mask" movement such as in the USA right now.
Trevlig resa!