Machynlleth on Wikipedia.

The former Bethesda Baptist Chapel (previously listed, incorrectly, as Bethania) on Heol Y Doll. SH 7445 0112. © John Bowdler. Coflein entry, which says that it was built in 1896. A 2009 Streetview. It was preceded by a chapel of 1838, which stood on Brickfield Street, and the site is visible on Streetview, here, now occupied by a pair of houses. Coflein entry.

Capel y Graig. This is a re-build in 1824 of an earlier chapel of 1789. It also underwent a restoration in 1875. SH 7469 0092. © John Bowdler. Coflein entry. Grade II listed.

Maengwyn Chapel (1867, Welsh Presbyterian). SH 747 008. © John Bowdler. Another view, © Chris Emms (2010). Coflein entry. Grade II listed.

St. Peter. Another view. SH 7455 0095. Both © John Bowdler. Interior view, © Kenneth Paver. Coflein entry. Grade II listing, which explains that, of the medieval church, only the West tower (C15) and belfy (1745) remain; the rest of the church is of 1827. A 2010 Streetview.

The former Tabernacl Chapel (Wesleyan, 1880), was successor to an earlier chapel of 1806, and is now a Museum of Modern Art (link). SH 7461 0091. © John Bowdler. The Coflein entry has more photos, including one of the interior. Another interior photo, taken during a concert, is available here.

Howard Richter has identified some further churches and chapels, as follows -
Machynlleth Community Church is the former Presbyterian Chapel (English-speaking, 1876). It stands on Heol Penrallt at SH 7458 0086. Streetview. Coflein entry.
St. Mair (R.C., 1959) on Heol Maengwyn. SH 7502 0087. Link. A 2010 Streetview. Coflein entry.
The former Salem Independent Chapel on Pentrehedyn Street had a short active life, 1840-1853. In the 1930's it was converted to serve as a meeting room for Capel y Graig, and is now known as Vane Hall. SH 7460 0073. The Coflein entry includes some photos.
A former Wesleyan Methodist Chapel (English-speaking) stands on Heol Maengwyn. Its dates are uncertain, but it seems to have been built in the mid-19th century, and closed before 1940. SH 7498 0081. A 2016 Streetview. The Coflein entry has some photos.
The following have all been demolished -
Capel Norton (Calvinistic Methodist) which stood on Maengwyn Street at SH 7486 0079. It shows as such on a map of 1889, but by the 1901 edition it had evidently been converted into a school. The Coflein entry dates it to 1784, and says it had been demolished by 1998. Housing now occupies the site, which is shown on a 2010 Streetview here.
Another Calvinistic Methodist Chapel stood on Poplar Terrace at SH 7447 0086. It shows on the 1888-9, 1901 and 1938 maps, but by the time of the 1948 edition the building had evidently been demolished. The Coflein entry describes it as a Mission Room. Howard suggests that some of the walls survive, based on these two Streetviews - 1, 2. To quote him directly,  "I surmise that the bases of two walls of the chapel building survive. The south wall ran across the back of the first view, from the car all the way to the road, from which point the west wall runs, in the second view, right-to-left across the foreground".
Christ Church (1881) stood on Maengwyn Street, on the site of the Public Library. A photo of the foundation stone (now preserved in the library) can be seen here. The church itself can be seen on an old postcard here. The 2010 Streetview shows that the original gate-piers survive from the church, as well as the metal railings seen at the extreme left of the postcard. It was closed in 1965 and demolished in 1967. Coflein entry.