Plain women in Tolkien are rare, but "plain-er" races exist.
Tolkien had no need to portray plain women as that was not what he was writing. He was writing about the great feats of Men and Elves in the West of Middle-earth as a mythology for England. Therefore, most of the women described are those of great power and beauty. Women who weren't were mostly either left out or hardly described. For example, most of the possibilities in the Lord of the Rings are merely of old women, who aren't described as plain or fair, but simply as old. Tolkien, however, did describe some races generally as either non-superlative or plain.
Hobbits were given quite a rudimentary description by Tolkien in 1938 when asked by Houghton Mifflin Co. to describe them.
I picture a fairly human figure, not a kind of 'fairy' rabbit as some of my British reviewers seem to fancy: fattish in the stomach, shortish in the leg. A round, jovial face; ears only slightly pointed and 'elvish'; hair short and curling (brown).
Letters of J.R.R. Tolkien: Letter 27, March/April 1938
Although not describing them as ugly, the description does not give the reader a hopeful feeling with the looks of Hobbits. With the non-superlative description given by Tolkien in 1938 as well as the examples in LotR and the Hobbit provide evidence of the plain nature Tolkien intended for his Hobbits.
And example of a female hobbit that's described as plain is Lobelia, but you need to reach the end of the story before you find that out.
Then there was Lobelia. Poor thing, she looked very old and thin when they rescued her from a dark and narrow cell.
Return of the King: Book Six - Chapter 9, The Grey Havens
Dwarven women are definitely the most consistently unattractive out of the races. (Assuming all of the evil races are male).
Tolkien describes Dwarves as being bearded. Regardless of age and gender. And unless one has a particular liking to bearded women. Most will agree that any descriptions would be non-superlative.
... no Man nor Elf has ever seen a beardless Dwarf - unless he were shaven in mockery, and would then be more like to die of shame... For the Naugrim have beards from the beginning of their lives, male and female alike, nor indeed can their womenkind be discerned by those of other race, be it in feature or in gait or in voice, nor in any wise...
The War of the Jewels
Men & Elves
Tolkien reserved his most prominent females as those with great power and beauty. This was often because his tales were centred around the "greatest" of the races. With the Silmarillion being a mostly a tale about the Noldor and the Silmarils, it also included some houses of Men, most prominently the Edain.
Within the races of Elves and Men Tolkien differentiated between various houses. With the Cali-quendi being the fairest of all the races, having been the only peoples to have seen the Light of the Two Trees. They were described as being the even more fair than their counterparts who did not cross into Aman. Furthermore, the Avari (those who did not answer the summons of the Valar and start The Great Journey") are described as the least fair of the Elves.
A similar comparison can be seen amongst the Houses of Men. The three Houses of the Edain who crossed the blue mountains and became Elf friends were considered to be more fair than the houses who did not. Some examples of fair women from the great houses are Nienor and Lindórië. The difference in the Houses is evident when you look at the descriptions of the Dunlendings and Druadan as opposed to the Edain women described in the First Age. Although only male descriptions are provided of the lesser houses, it would be very unlike Tolkien to make large differences within peoples.