Taking a slightly different approach, and guessing that some knowledgeable folk will probably suggest many solid (and well worth reading) classics, I thought I’d suggest a few more recent authors I’ve enjoyed recently.
English author Richard K Morgan is the first, particularly his dystopian near-future novels Market Forces and Black Man (published in the US as Thirteen). You may also enjoy his Takeshi Kovacs novels (named for the main character), Altered Carbon, Broken Angels, and Woken Furies, which although set further future are very human-based, (space and aliens are more minor themes), with a strong “noir” feeling.
Slightly further out, but again with very human themes, are some of Jack McDevitt’s novels, particularly his Alex Benedict books (A Talent for War, Polaris, and Seeker… so far). McDevitt’s themes in these (fairly far future) stories are around archaeology, so set far in the future and digging up the past (still our future). His other main series, (called the Academy Series or the Priscilla “Hutch” Hutchins series) is more around xeno-archaeology, but shares some similar characteristics.
John Scalzi is third, his Old Man’s War being reminiscent of both Heinlein and Haldeman (though it definitely does involve space and aliens), and I was caught from the opening line: “I did two things on my seventy-fifth birthday. I visited my wife’s grave. Then I joined the army.” The sequels were also enjoyable, and I’m currently enjoying his (unrelated) novel The Android’s Dream.
Last, though certainly not least, is another English author Neal Asher. His Polity universe novels, both the Ian Cormac and Spatterjay books, are set far, far future, and definitely involve space and aliens (although not intelligent aliens to a great degree), but are great reads nonetheless, and have strong themes around what it is to be human, particularly in a high tech environment where there are artificial intelligences, augmented humans, human/AI hybrids, ex-human consciousnesses in robotic bodies, etc.