As the books call it, Elrond's house is the Last Homely House east of the Sea. But if Rivendell is the last homely house, what are the other homely houses east of the sea? Or does Rivendell count as the last and the first because it is the only one? This question has bugged me for a while, and I would be very happy if there is a reliably-based answer to it (i.e. not something that the movies say).
Homely here just means civilized and decent, and is more of a description than an official category
In the original manuscript of The Hobbit, this was named the "Last Decent House".
They asked him where he was making for. ‘You are now at the very Edge of the Wild’ he answered. ‘Somewhere ahead is the Last Decent House – I have been there already and they are expecting us.’
Marquette Tolkien Mss 1/1/3, published in The History of The Hobbit
Likewise, in The Annotated Hobbit, Douglas Anderson points out that "homely" means a place where you're treated kindly.
In describing Elrond’s house as homely, Tolkien refers to what the Oxford English Dictionary describes as “characteristic of home as the place where one receives kind treatment; kind, kindly.”
The Annotated Hobbit - Chapter 3 - "A Short Rest"
The implication that Tolkien is saying is that up to this point you're still part of the more civilized home turf, past here you enter "The Wild" and start your real adventure. Corey Olson explains this in Exploring J.R.R. Tolkien's The Hobbit.
Rivendell is called "The Last Homely House," and it stands on an important boundary. It is at the border, with all of the "respectable country," where one might possibly find good inns, to the west (30). When you get to Rivendell, as Gandalf explains to Bilbo, you have "come to the very edge of the Wild" (44). As I mentioned in Chapter Three, Rivendell doesn't just sit on this boundary; it embodies it. The house of Elrond is the place where the world of quiet comforts and the world of legends come together and coexist. The path beyond it, into the Wild, is "a hard path and a dangerous path, a crooked way and a lonely and a long" (52).
Exploring J.R.R. Tolkien's The Hobbit - Chapter 4 - "Over the Edge of the Wild"
As John Rateliff points out in The History of the Hobbit, this was probably inspired by the Cottage of Lost Play from Tolkien's earlier writings.
This brief chapter contains the most explicit references yet linking The Hobbit to the mythology out of which it grew. Elrond and Gondolin come directly from the Silmarillion tradition, while the ‘Last Decent House’ (renamed the Last Homely House before the end of the chapter) is clearly inspired by the Cottage of Lost Play that had appeared in the frame story of The Book of Lost Tales, where ‘old tales, old songs, and elfin music are treasured and rehearsed’ (BLT I.20) – a description strikingly like that of Elrond’s house, which ‘was perfect, whether you liked food or sleep or work or storytelling or singing or just sitting and thinking best’ (p. 115), and of which the narrator says ‘I wish I had time [to] tell you even a few of the tales or one or two of the songs that they heard in his house’ (ibid.). It is in the House of Lost Play (as it is also called; cf. BLT I.189) that Eriol the wanderer hears all the stories that together make up the ‘Lost Tales’, just as much later it is in Elrond’s House (not yet named ‘Rivendell’)1 that Bilbo in his retirement collected the stories that made up The Silmarillion (cf. LotR.26–7 & 1023).
The History of The Hobbit - "The Last Decent House"
To more specifically answer your question, some other examples of "Homely Houses" would be various inns like The Prancing Pony, or perhaps even private residences like Bag End.