When and where did "bad boy" start being used to mean something impressive, e.g. "Let's take this bad boy out for a spin!"

Solution 1:

OED, in the entry for bad boy, n.,

2. colloq. (chiefly U.S.) (orig. in African-American usage). Something considered extremely effective or impressive.

attests use of the sense as early as 1969:

1969 Afro Amer. 10 May 31/5 The [Howard University] administration has been selling (wolf) tickets with their TRO's (Temporary Restraining Orders) all year; and the students just cashed in one of those bad boys!

Prior use of the phrase in the given sense can be assumed; it follows on the more general use of 'bad' in the sense of 'good', attested in the OED entry for bad, adj., n.², and adv. from 1897:

IV. slang (orig. U.S.). Formidable, good. (Sometimes with repeated vowel, for emphasis.)

12. As a general term of approbation: good, excellent, impressive; esp. stylish or attractive.

  1897 G. Ade Pink Marsh 195 She sutny fix up a pohk chop 'at's bad to eat.

The 'impressive' sense of 'bad boy', however, describing things, owes a greater debt to its immediate progenitor, the archetypal 'bad boy', attested from 1860 in OED:

1. colloq. (orig. U.S.). A man who does not conform to expected or approved standards of conduct; a rebel. With of or genitive indicating the sphere in which he is so regarded.

1860 N.Y. Times 9 Mar. 4/3 We of New York who do duty so constantly in the British Press as the model ‘bad boys’ of Christendom.

These 'bad boys', often ambivalently regarded, have been immortalized in literature: Thomas Bailey Aldritch's 1869 The Story of a Bad Boy; George W. Peck's 1883 Peck's Bad Boy and His Pa, along with its sequels; Mark Twain's 1884 The Adventures of Huckleberry Finn.

Solution 2:

The idiomatic expression definitely originated in AmE according to the following sources, probably from the early '70s. The New Partridge Dictionary of Slang and Unconventional English cites a usage from 1974:

Bad boy:

• something that is impressive US - I finally got this bad boy together bout six, seven months. Got the whole place furnished top to bottom. — Vernon E. Smith. The Jomes Man, p.139 - 1974.

while the Green's Dictionary of Slang cites a usage from the early '80s:

Bad boy:

(US) anything considered impressive.

• 1983 [US] R. Price Breaks 156: Tell them to get it the hell out of room 220 so I can move in the way I was supposed to, and this bad boy’s yours.

a usage with a related meaning, from which the above usage might derive, is from black American and dates from the '50s:

bad boy:

(US black) a general term of approval, referring both to individuals and to objects.

• 1953 [US] L. Durst Jives of Dr. Hepcat (1989) 9: When I pin you daddio the wagon in here, and you lodes my heart on. You don’t pack no six gun, but you are a bad bad boy, and for you my lid always flip.