List of stations that broadcast "Out of This World"

[TMC]

Obviously, Out of This World during its first season, at the very least, aired on NBC's owned and operated stations as part of its "Prime Time Begins at 7:30" experiment:
City Station

• Atlanta WAGA 5[8]
• Boston WCVB 5[9]
• WFXT 25[10]
• WLVI 56[11]
• Charlotte WBTV 3[12]
• Charleston, South Carolina WTAT 24
• Charleston, West Virginia WVAH[13]
• Chicago WMAQ 5[14]
• WPWR 50[15]
• Cleveland WUAB 43
• Davenport KWQC 6[16]
• Detroit WXON 20
• Durham WPTF 28[17]
• Fairbanks KTVF 11[18]
• Fort Worth KTVT 11
• Grand Rapids WXMI 17[19]
• Greenville WFIX 8[20]
• Hartford WTIC 61[21]
• Houston KHTV 39
• Indianapolis WXIN 59[22]
• Jacksonville WJXT 4[23]
• Los Angeles KNBC 4[24]
• KTLA 5[25]
• Miami WDZL 39[26]
• Milwaukee WVTV 18[27]
• Minneapolis KITN 9
• New York WNBC 4
• Oakland KTVU 2[28]
• Omaha KPTM 42[29]
• Paris, Ontario CIII 6[30]
• Philadelphia WPHL 17[31]
• Salt Lake City KXIV 14[32]
• San Juan WAPA 4[33]
• Seattle KSTW 11[34]
• Secaucus WWOR 9[35]
• Sacramento KRBK 61
• Spokane KAYU 28[36]
• St. Louis KPLR 11[37]
• Washington, D.C. WFTY 50[38]
• WRC 4[39]
• Wichita KSAS 24[40]

[tvvideotrader]

San Diego: Season 1: KGTV-10; Seasons 2-3: KUSI-TV 51; Season 4: KTTY-TV 69

[KonfusionFTC]

Is it currently airing on anything?

[KurtfromPitts]

In Pittsburgh WTAE ran OOTW back-to-back with Small Wonder on Saturdays in 1987-88. OOTW briefly turned up on WPGH in the Fall of 1989.

[TMC]

Somebody here, also said that they recall seeing Out of This World in Dallas on channel 27, which would've been KDFI as well as channel 11 (KTVT).

Here's some print ads from its first season as part of NBC's "Prime Time Begins at 7:30" experiment:




And another one from the Sacramento affiliate: