Absolutely agree with everyone else that 7 days in the city is too much.

If you want to get away from the city and into nature, the 7-day itinerary you linked is good. Hunnebostrand, Smögen, and Fjällbacka are all nice places. South of Gothenburg, you could consider Varberg and Båstad.

Otherwise, both Stockholm and Copenhagen are easy 4-hour (-ish) train trips from Gothenburg.