Locations from # 13.06 (DVD count) / 12.06 (original count):
The Western town where Ellie and Clayton arrive is Laramie Street at Warner Bros. Studios, 4000 Warner Boulevard, Burbank, CA 91522. This was the last standing western set at The Burbank Studios / Warner Bros. at the time; it was demolished in 2003. It was located where nowadays Warner Village sits (a suburban-style anywhere-USA-type residential street that has real homes that serve as production offices, but are photogenic for exterior filming).
Just as a side note, back in the day when "Dallas" was shot, Warner had just fought off Lorimar's attempt of a takeover and, after merging with Time Inc., Warner Communications bought out Lorimar in turn (January 21, 1989). That's why many Lorimar shows filmed a lot more scenes at TBS / WB again in the 1989-90 season and beyond -- simply a matter of trimming down costs. In the complex transactions following WB's takeover of Lorimar, WB and Columbia dissolved their partnership in The Burbank Studios, which put WB back in control of TBS (now renamed WB Studios and Warner Bros. Ranch, the latter being the ex-Columbia Ranch) while Columbia became the owner of Lorimar Studios (previously MGM) in Culver City. Columbia, by the way, had just been sold by its parent company, Coca-Cola, to Sony at the time. A widely spread myth claims that settling a legal battle between WB and Sony over certain producers was the reason for transferring ownership of Lorimar Studios to Columbia, which was not the key factor though. It was basically a regulatory matter because a conglomerate consisting of WB and Lorimar plus Columbia (via their TBS joint venture) was out of the question from the standpoint of anti-trust laws.
Anyway, this was WB's Laramie Street:
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The establishing shot of the Paradise Motel where Clayton and Ellie are staying is stock footage of the motel by the same name (not a prop sign) located at 1116 West Sunset Boulevard, Los Angeles, CA 90012:
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