American reading of the British expression "look around impressively"

I hate to contradict your writers' critique group, but that is a perfectly fine phrase in American English. The only plausible criticism I could imagine is that it might sound slightly old-fashioned, but I'm not even sure about that.

If you nevertheless decide to use an alternative expression, the choice should be guided by what character trait you are trying to emphasize. Some possibilities are (all links are to Merriam-Webster) self-importantly, pompously, arrogantly, pretentiously, grandiloquently, haughtily, conceitedly, grandiosely, superciliously, pontifically, snootily, affectedly, overbearingly, imperiously, smugly, and no doubt many others.

Discussion

If you search google books for "looked around impressively" (here), you will see several examples of this phrase in published literature, including works by American authors.

Some examples of usage by American authors:

He looked around impressively.
From Myra Page, Gathering Storm: A Story of the Black Belt (1932) (link)

Willie looked around impressively at the deeply attentive Troop members.
From Myra Reed Richardson, The Mule Skinners (1945) (link)
(If you search for color and center, you will find hits, but not if you search for colour and centre. Also, Viking is an American publishing house.)

He looked around impressively.
From Herbert Brean, The Clock Strikes Thirteen (1954). (link)

He looked around impressively.
From Harry Kemelman, Friday the Rabbi Slept Late (1964) (link)

A portrait of Olivier, given to him by Sir Larry, broods impressively.
From David Ansen and Abigail Kuflik, 'America's own. (cover story)', Neewsweek magazine (1994), via COCA (Corpus of Contemporary American English)

You know how many millennia it's been since that idiot Tower crumbled into dust? He flicked his golden wings imperiously, impressively.
From Harlan Ellison, From A to Z, in the Sarsaparilla Alphabet (link) (2001), via COCA

Looking for something positive to say, I pointed to a corner shelf. "I like the little glass monkey. " Aunt Lilith frowned. " Don't you remember? Olivia brought that monkey to me from Scotland. " " How could I forget? " I whispered under my breath. " Olivia went with her class to Scotland. She's a sophomore at Vandergriff High. " Aunt Lilith nodded impressively. " Olivia, tell Bea your news. " I made cheerleader this year, " Olivia said, folding her hands neatly in her lap. " Such a pretty girl. " Aunt Lilith beamed at Olivia.
From The Pretty One (2008), via COCA

For completeness, here is the relevant entry in the Oxford English Dictionary (OED):

impressively, adv.: In an impressive manner; in a way fitted to impress.

<sup>1818 in H. J. Todd Johnson's Dict. Eng. Lang.

1830 I. D'Israeli Comm. Life Charles I III. vi. 110</sup>
The King..impressively assured him that he considered him the happiest man in England.

^{1841 J. W. Orderson Creoleana xvii. 209}
The funeral service was impressively performed.

^{1860 J. Tyndall Glaciers of Alps i. xvi. 115}
My guide..repeating the warning more impressively before I attended to it.