After all these years of using the Tokyo Limousine Bus as well as the Narita Express (both of which runs ~ 3500 Yen) I just discovered that there is a cheaper alternative from two locations: Tokyo Station and Ginza.
I walked by the designated pickup point for the Keisei Bus service in Ginza, and it piqued my interest that quite a few people were lining up, so I looked at the schedule and got one of their flyers.
Getting to Tokyo’s airports from Ginza has always been somewhat challenging, at least in recent years, as the orange Friendly Limousine Bus has drastically reduced its schedule (for a long time after COVID there was no bus at all), and Ginza is far from the Narita Express Line.
The Keisei-branded transportation options to Narita are both considerably cheaper than the Limousine Bus and NEX.
Keisei Skyliner to/from Ueno Station costs a third of what the NEX charges, with the caveat that you have to change trains in Ueno unless you stay near there.
The Keisei Bus from Ginza Station or Tokyo Station costs 1,500 yen per person, 65% cheaper than the Limousine Bus competition, but also takes a little longer, as far as I can judge from the schedule.

Keep in mind you have to pay this bus in cash or with SUICA/PASMO cards. Credit cards are not accepted, although you can charge your SUICA in the mobile wallet via credit card.
This is a very interesting alternative for me the next time I’m staying at the Centric Ginza or one of the surrounding hotels.
In this case, I went back to Shibuya, where I stayed at the Indigo, and later in the evening caught the Narita Express to Narita City, as I was staying at the Narita Hilton. It’s also 1000 yen cheaper to get off at Narita rather than a little bit further to Narita Airport Terminal 1/2 and most of the hotels have a shuttle bus from Narita Station.
Conclusion
Transportation options from Tokyo to Narita and vice versa have always been a bit of a challenge. Less so because of the expense (especially now with the weak Yen), but also because of the distance.
I’m now using a mix of the Limousine Bus, but most of the time I still get the Narita Express because you won’t get stuck in traffic with that. As long as you stay anywhere around a NEX stop you’re golden.
This Keisei Bus, however, is a budget-friendly option if you don’t want to spend 3,600 Yen per person, as long as Ginza or Tokyo Station works for you. For the Ueno area, you can also use the Keisei Skyliner train.
What is your preferred method for transportation between Narita and Tokyo?