When the Great Northern War broke out in 1700 the main Swedish fortresses in Ingria were Narva, Nyen and Nöteborg, in Estonia Reval and in Livonia Riga, Neumünde, Pernau and Riga. In Ingria substantial amounts had been spent on Narva, while the only major work done at Nöteborg during the latter part of the 17th century was the rebuilding of the so called "Black Tower". One cannot help wonder what would have happened if Czar Peter in 1700 had attacked Nöteborg and Nyen rather than the much more formidable Narva. Most likely had been able to capture them both rather quickly, totally changing the situation facing Charles XII when he landed at Pernau in early October. In such a scenario a foray into Courland and involvement in the Lithuanian civil war could well have appeared less appealing to him, but on the other hand it would have been both expensive and difficult to supply a large army in Livonia (and even more so in Ingria) for operations against the Russians.
It is worth noting that the Saxon's did not particularly like the Czar's decision to attack Narva as they considered the fortress to be part of Estonia, which according to the agreements made before the war was off limits. However, Peter could rightly point out that Narva administratively belonged to Ingria. When Russian forces in 1704 captured Dorpat there was no question - the Czar had reached beyond what the agreements said. For the time being the matter was settled by a manifesto in which Peter stated that he had taken the town on behalf of the Polish Crown and assurances that the matter would be settled in the promised fashion.
Perhaps some of this uncertainty around the Czar's real intentions were a contributing factor in the peculiar episode called "the Ketten affair". In late 1702 Johan Reinhold Patkul visited Vienna, where he received a letter from a close associate of Jakub Sobieski, a clergyman called Ketten. Ketten asked Patkul about the Czar's view of Sobieski and suggested that Charles XII was prepared to grant Patkul amnesty if the latter could convince Peter to make peace with Sweden. Patkul replied with the interest, suggesting a personal meeting between him and Ketten. Apparently this went well enough and Patkul later wrote to Ketten saying that he was prepared to make an attempt to carry out his part of the deal if he received written assurances from Charles XII. However, no such document was issued (and it's unlikely that Charles was informed of Ketten's action). The mysterious incident ended with King Augustus warning the Czar about Patkul's intrigues - he was a man who only worked for his own benefit and couldn't be trusted.
Erdmann, Y., Der livländischen Staatsmann Johann Reinhold von Patkul. - Berlin, 1970.