Jesus clearly refers to a very unpleasant place in e.g. Mark 9:47–48[1], Luke 16:24,[2] and Matthew 25:41[3] (where it's explicitly stated that false prophets will go to the same place as "the devil and his angels"). Other references to an unambiguously bad place, as the sole and final destination of unbelievers, are throughout the New Testament, e.g. the "lake of fire" in Revelation 20:15[4] and 21:8[5]. Revelation 20:14[6] even says that "Hades" will be thrown into that same "lake of fire" (which of course supports what you're saying about Hades being distinct from Hell). As a final note, even the reference to Tartarus in 2 Peter 2:4 speaks of it as a temporary holding place where "angels who sinned" are being "kept for judgment", implying that there's a more final fate awaiting them (identified in Revelation 20:10[7], at least for Satan, as the aforementioned "lake of fire").
The main point I'm trying to make is that, while it's certainly true there are other "places where dead people/angels go" than Heaven and Hell, that's only true at this point in time. To my knowledge, the New Testament is consistent about a final judgment where there are only two possible fates (the New Jerusalem, i.e. Heaven, and the lake of fire, i.e. Hell).
[0] "For if God did not spare angels who sinned, but cast them into the pit [Tartarus] and delivered them to chains of darkness, being kept for judgment;"
[1] "And if your eye causes you to stumble, gouge it out; it is better for you to enter the kingdom of God with one eye, than, having two eyes, to be cast into hell [Gehenna], where their worm does not die, and the fire is not quenched."
[2] "And he cried out and said, ‘Father Abraham, have mercy on me, and send Lazarus so that he may dip the tip of his finger in water and cool off my tongue, for I am in agony in this flame.’"
[3] "Then He will also say to those on His left, ‘Depart from Me, accursed ones, into the eternal fire which has been prepared for the devil and his angels;"
[4] "And if anyone’s name was not found written in the book of life, he was thrown into the lake of fire."
[5] "But for the cowardly and unbelieving and abominable and murderers and sexually immoral persons and sorcerers and idolaters and all liars, their part will be in the lake that burns with fire and brimstone, which is the second death."
[6] "Then death and Hades were thrown into the lake of fire. This is the second death, the lake of fire."
[7] "And the devil who deceived them was thrown into the lake of fire and brimstone, where the beast and the false prophet are also, and they will be tormented day and night forever and ever."