What LGR-encoded Greek fonts are available?

$ find /usr/local/texlive/2019/texmf-dist -name lgr\*fd | wc -l
42

so there are 42 font families in texlive 2019 already set up for Greek LGR encoding. If you include use of tools such as ofttotfm than would let you convert otf fonts to an LGR encoded subset there will be hundreds if not thousands of available fonts.

The list from running find is

./tex/latex/cbfonts-fd/lgrcmr.fd
./tex/latex/cbfonts-fd/lgrcmro.fd
./tex/latex/cbfonts-fd/lgrcmss.fd
./tex/latex/cbfonts-fd/lgrcmtt.fd
./tex/latex/cbfonts-fd/lgrlcmss.fd
./tex/latex/cbfonts-fd/lgrlcmtt.fd
./tex/latex/cbfonts-fd/lgrlmr.fd
./tex/latex/cbfonts-fd/lgrlmro.fd
./tex/latex/cbfonts-fd/lgrlmss.fd
./tex/latex/cbfonts-fd/lgrlmtt.fd
./tex/latex/cm-lgc/lgrfcm.fd
./tex/latex/cm-lgc/lgrfcs.fd
./tex/latex/cm-lgc/lgrfct.fd
./tex/latex/comfortaa/lgrfco.fd
./tex/latex/droid/lgrfdm.fd
./tex/latex/droid/lgrfdr.fd
./tex/latex/droid/lgrfds.fd
./tex/latex/epigrafica/lgrepigrafica.fd
./tex/latex/gentium-tug/lgrgentium.fd
./tex/latex/gfsartemisia/lgrartemisia.fd
./tex/latex/gfsartemisia/lgrartemisiaeuler.fd
./tex/latex/gfsbaskerville/lgrgfsbaskerville.fd
./tex/latex/gfsbodoni/lgrbodoni.fd
./tex/latex/gfscomplutum/lgrcomplutum.fd
./tex/latex/gfsdidot/lgrudidot.fd
./tex/latex/gfsneohellenic/lgrneohellenic.fd
./tex/latex/gfsporson/lgrporson.fd
./tex/latex/gfssolomos/lgrsolomos.fd
./tex/latex/kerkis/lgrkfn.fd
./tex/latex/kerkis/lgrmak.fd
./tex/latex/kerkis/lgrmaksf.fd
./tex/latex/lxfonts/lgrllcmss.fd
./tex/latex/lxfonts/lgrllcmtt.fd
./tex/latex/miama/lgrfmm.fd
./tex/latex/opensans/lgrfos.fd
./tex/latex/opensans/lgrfosj.fd
./tex/latex/tempora/lgrtempora-tlf.fd
./tex/latex/tempora/lgrtempora-tosf.fd
./tex/latex/txfontsb/lgrtxr.fd
./tex/latex/txfontsb/lgrtxrc.fd
./tex/latex/txfontsb/lgrtxry.fd
./tex/latex/txfontsb/lgrtxryc.fd

David has listed quite a few possibilities. Here I want to highlight two that I find particularly interesting.

Gentium

Gentium is an award winning font that supports a wide array of Latin scripts as well as Greek an Cyrillic. You can use it with:

\usepackage{gentium}

Note that I had to use "c" instead of "s" to get the correct final sigma (thanks to @Thérèse for spotting this).

GFS Didot

GFS Didot is a free and faithful digital version of Didot's Greek, a.k.a. "apla". GFS has paired the Greek glyphs with Palatino like Latin glyphs, which I do not particularly like. I like the combination with Palatino, though:

\usepackage[sc]{mathpazo}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{udidot}
\linespread{1.05}

The sc option can be replaced with osf to get old-style/lining figures. Some might claim that Pagella is the better choice for Palatino, but I have preferences.

Times

In the comments you mention, that you are using newtxtext, i.e. Times, as text font and that you like GFS Didot. Unfortunately, GFS Didot is to dark compared to Times, but you can try other fonts, e.g.

\usepackage{newtxtext}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{txr}

Here the Times plus GFS Didot combination, that I do not recommend, with full example code:

\documentclass[a4paper,12pt]{article}
\usepackage[greek.ancient,italian]{babel}
\usepackage[T1]{fontenc}
\usepackage{newtxtext}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{udidot}
\begin{document}
Dal greco\begin{otherlanguage*}{greek}
br\'aqistos
\end{otherlanguage*}(brachistos), e\begin{otherlanguage*}{greek}
qr\'onos
\end{otherlanguage*}(chronos), tempo.
\end{document}

At the answer of the user @RalfStubner and best user @David Carlisle I add:

porson (greek)

\documentclass[a4paper,12pt]{article}
\usepackage[greek.ancient,italian]{babel}
\usepackage[T1]{fontenc}
\usepackage{newtxtext}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{porson}
\begin{document}
Dal greco\begin{otherlanguage*}{greek}
br\'aqistos
\end{otherlanguage*}(brachistos), e\begin{otherlanguage*}{greek}
qr\'onos
\end{otherlanguage*}(chronos), tempo.
\end{document}

Artemisia

\documentclass[a4paper,12pt]{article}
\usepackage[greek.ancient,italian]{babel}
\usepackage[T1]{fontenc}
\usepackage{newtxtext}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{artemisia}%%%%% You must delete from %%%lgrartemisia.fd, lgr to have only artemisia. Same for every font of the list of %%%@David Carlisle.
\begin{document}
Dal greco\begin{otherlanguage*}{greek}
br\'aqistos
\end{otherlanguage*}(brachistos), e\begin{otherlanguage*}{greek}
qr\'onos
\end{otherlanguage*}(chronos), tempo.
\end{document}

If there are others I can add, I am glad you can edit my answer. Greetings and thanks to all of you.