Getting around Greater Seoul is efficient and cheap with public transport. A T-Money Card is highly recommended. One can easily reach Namhansanseong by Seoul Metro, transferring to bus - the latter are well-kept and provide excellent Wi-Fi. On weekends, get off at Sanseong metro station and transfer to bus 9-1. From Mondays to Fridays, either transfer to bus 9 there or transfer to bus 9 or 52 at Namhansanseong metro station. To beat the crowds, avoid the weekends!
My visit was on a Wednesday in late March 2024 and was not crowded at all. I started at Haenggung/Namhansanseong Palace, then walked to Bukmun/North Gate and from there counterclockwise close to the outer walls. Just before reaching Seomun/West Gate, at the northernmost point of the wall, one can exit at "Secret Entrance No. 5" to reach "Yeonjubong Ongseong", the watchtower with the panorama that GabLabCebu shared. I agree with the fellow WHS traveller that this is the first highlight, followed by Sueojangdae/West Command Post [picture].
Overall, despite the leafy setting, I found this site to be less picturesque than the Suwon City Walls/Hwaseong Fortress. The distances to walk are very similar to Suwon and so are the ascents and descents. Please note that vending machines can only be found close to Haenggung/Namhansanseong Palace, so bring enough beverages. One does not need to walk the full loop but may shortcut by taking a bus 9 or 52 back to the metro stations from the bus stop closest to Nammun/South Gate.