You might try James S. A. Corey’s “Expanse” trilogy. (Leviathan Wakes, Caliban’s War, Abaddon’s Gate). It’s limited to the solar system but has a good “space opera” feel.
Then there’s H. Beam Piper. For pure Space Opera try Space Viking or The Cosmic Computer.
And I know I’m not supposed to like him, but I’ll add Alexei Panshin’s Anthony Villiers novels (Star Well, Thurb Revolution and Masque World)
Lois McMasters Bujold has the Miles Vorkosigan series. Try The Warrior’s Apprentice and The Vor Games to see if you enjoy her style.
Definitely the Vorkosigan series by Lois McMaster Bujold.
eta: You know, like Reepicheep said.
Don’t forget Sybly Whyte! 
Was all set to mention The Culture and Revelation Space, and then saw you’d included Banks and Reynolds… You have mentioned Niven/Pournelle; did you make it through all of the Man/Kzin Wars Series?
Would Vernor Vinge’s, A Fire Upon The Deep, count? Hugo Award winner, after all.
I’ll recommend Charles Stross’s two contributions to the genre that I’ve read: Singularity Sky and Iron Sunrise. Neat universe, that he unfortunately won’t be revisiting. Accelerando and Glasshouse from him are also supposed to be good.
I tried getting into The Quantum Thief, based on Stross’s blurb for it, and couldn’t get into it. Probably too smart for me, but the beginning of it is an interesting take on the Prisoner’s Dilemma.
I particularly enjoy Poul Anderson’s Flandry series. A Naval Intelligence officer striving to keep the Empire from falling into chaos and “the dark night”.
Don’t forget A. Bertram Chandler’s endless “Rimworld” and Grimes series
There’s also the swonderfully weird “Professor Jameson” series of Neil R. Jones (which was mentioned in the anime Ghost in the Shell). Anime loves some space opera.
This. Sometimes you don’t want modern sensibilities. You want colliding galaxies and planets used as weapons and massive ships thundering through the ether and…
You get the idea. Kimball Kinnison rocks!
Not enough things coruscate these days.
I take Brain Glutton’s comment on the style - even reading them in the 70s, the social setting was very dated - barely into the 50s, if that. But, it really fits the OP’s specs.
[QUOTE=JohnT]
I prefer tales of interstellar civilizations - it’s the rare novel that’s set in a solar system that I like
[/QUOTE]
The Lensmen (note - always Lensmen, with one exception; the books make it clear that women just aren’t up to the challenge of wearing a Lens, poor little things. As I said, barely into the 50s…) are flying all over the two galaxies (yes, two galaxies; one wasn’t enough for Smith’s vision). In fact, in one of the books, Kinnison is in the asteroid belt around Sol and is leaving for Earth. He comments that it’s weird to be taking such a short trip that you can actually see your destination with the naked eye before you leave. That should give you an idea of the scale of the series.
[QUOTE=]
If you read them though, don’t read Triplanetary first – it gives away the game.
[/QUOTE]
I started with Triplanetary, and I didn’t think it gave away the game, any more than the opening scenes on Trantor did for Asimov’s Foundation series - both set the canvas for the whole series. Plus, in each of the succeeding books, Smith has a summary right at the start, so it’s pretty hard to avoid reading the outline.
meh. He was just a hack writer.
But, I see he does have a profile on zoominfo, c/o Kinnison & Co. LLC.
More Patrick O’Brien or CS Forester than Tom Clancy. If you don’t like nautical fiction, then skip it.
How about the “Old Man’s War” books by John Scalzi? The military angel is less of a focus than the alien civilizations encountered and the exploration of transferring one’s mind into enhanced bodies (I really want a “BrainPal”!)
I’ll second the Expanse trilogy recommendation. Lots of heroes rocketing from place to place to rescue heiresses and little children from strange threats to humanity and government cabals. Still waiting on the last book though.
C.J. Cherryh, for sure. The Chanur novels already mentioned are quick and very good. My favorite is the Faded Sun trilogy, and some of her standalone books like Cuckoo’s Egg or Serpent’s Reach.
Also, Gene Wolfe. Particularly The Book of the New Sun and The Book of the Long Sun. Although both probably fall into the “action happens within the same system”, they’re both amazingly good.
You might like Zelazny’s “Amber” series. It isn’t exactly *space *opera, more of a “universe-opera” with characters gallivanting through the multi-verse in search of glory, power, and revenge.
Jack Vance’s “Demon Princes” series includes lots of planet-hopping, criminals, foreign cultures, kidnapping, skullduggery, hand to hand combat, damsels in distress, and other fun stuff that might trip your trigger.
Note that these ain’t easy readin’. They’re worth it, but they’re extremely dense and challenging. I tend to think of space opera is a bit fluffier, so that’s why I mention.
Um, the John Carter Of Mars series by Edgar Rice Burroughs anyone?
How about Cordwainer Smith? His works are hard to categorize and I think of him as an acquired taste, but once you’ve acquired that taste, you’ll want more. I’m not sure if many of his stories would fit your definition of space opera, but give him a try. And I definitely agree with the recommendation to try Star Kings by Edmond Hamilton. I think that’s the first science fiction I ever read, more than 50 years ago, and it started me down a path I continue to enjoy.
Hardly “interstellar.” 
Doesn’t make it any less good, of course.
For that matter when I was younger I was a big fan of Poul Anderson’s Polesotechnic League/van Rijn books. Lot of heroic derring-do and starship combat.