Stephen King’s 11/22/1963 is a book I would recommend to anyone.
Then I second the recommendations of Time and Again (a classic, which also has mystery and romance elements) and If I Never Get Back (provided you like baseball).
Lest Darkness Fall, by L Sprague de Camp.
There’s a sequel: From Time to Time.
You might like H. Beam Piper’s Lord Kalvan of Otherwhen even though it’s technically not time travel. A Pennsylvania state trooper is accidentally picked up by a dimensional traveler, and dropped off on a parallel Earth that’s technologically still at a Renaissance level. His limited knowledge of science (in particular, the manufacture of gunpowder and firearms) makes him a very important man.
Oh, and here’s another vote for Finney’s Time and Again. A friend of mine once described it as “science fiction for non-science fiction fans.”
Seconding Anubis Gates. Not sci-fi, exactly. More of a steampunk fantasy but really, really good.
Also recommending The Mummy, Or Ramsey The Damned by Ann Rice. In this, the mummy time travels to 1914 and must come to terms with that times, ah, times.
My wife likes “Time and Again”, and she hates SF.
Was a very good book. 
Deborah Harkness’ *All Souls Trilogy. * The middle book especially fits the criteria of the OP exactly. Ignore the supernatural creature angle, it works in book and isn’t annoying.
Jodi Taylor’s Chronicles of St Mary’s fits the bill and the books are funny and a cracking good read all through.
Seconded. I couldn’t put it down. Although I believe it’s just called 11/22/63.
I agree. This was only my second King book, having only read Under the Dome previously (which wasn’t quite as stinky as the miniseries, but still boring). Still, I have to think I’d have found a better way to stop Oswald, such as calling the freaking Secret Service.
The best in that genre is probably the classic Lest Darkness Fall.
It is often cited as the inspiration for many, many modern authors.
The set-up is very simple: a man who is an expert in Roman History gets zapped back to 5th century Rome, during the era of the invasion of Gothic Italy by the Byzantine general Belisarius … and attempts to actively change the course of history.
It’s compulsive readable and sounds like exactly what you are looking for.
Edit: the actual method of “zapping” isn’t explained. It just happens. So no science-fiction whatsoever (at least, not much).
A thousand times this. Not your standard time travel tale it’s great.
If you run across Leo Frankowski’s “The Cross Time Engineer”, keep on running. It is nothing but the most blatant masturbatory MarySue-ism ever put on paper.
Personally I think King’s 11/22/63 became very long winded. The domestic problems of the Oswalds became tedious fairly quickly but it was still an enjoyable read. Years ago I really enjoyed Stanley Shapiro’s A Time To Remember:
David Russell, a Dallas schoolteacher is still in mourning for his older brother who was killed in Vietnam twenty years before. He meets eccentric physicist, Dr. Hendrik Koopman who has built a time machine. Russell convinces Dr. Koopman to send him back to November 22, 1963 so that he can stop Lee Harvey Oswald from killing Kennedy, certain that had JFK lived, there would have been no Vietnam War.
Aw, you’re just jealous because
you couldn’t build a fleet of fighter planes in 13th-century Poland.
And it’s available in a nice collection with several stories that were inspired by it (including Pohl’s “The Deadly Mission of Phineas Snodgrass”) https://www.amazon.com/Lest-Darkness-Fall-Related-Stories-ebook/dp/B004Q9U4S4#nav-subnav
I liked it.
The Tiffany Aching stuff gets a bit Mary Sue-ish, but the only contender I know of for Frankowski’s title is the whole Mortal Instruments series, where the Mary Sue is named Claire and the author’s last name is CLARE. Move along, nothing to see here…
If you don’t mind something that’s tongue-in-cheek and set a bit earlier than the range mentioned in the OP, there’s Harry Harrison’s The Technicolor Time Machine: a scientist gets funding for his time-travel experiments from a Hollywood producer whose goal is to shoot a drama about the Vikings’ discovery of Vinland (America)… on location, with real Vikings.
The Guns of the South by Harry Turtledove, in which a group of people from the 1990’s go back to the American Civil War to help the South win.