Dear kristinet,
Definitely as jjkdc mentioned, the Museo Archeologico is closed on Tuesdays.
http://www.marketplace.it/museo.nazionale/emuseo_home.htm
Also as jjkdc and Peregrin_man mentioned, it would be in your best interest to head to Pompei Scavi first and then to Napoli so that you wouldn't need to backtrack to Pompei Scavi and then back to Napoli to catch your train to Firenze.
Going museum or Pompei Scavi first can depend on your tastes. I personally think it's nice to see Pompei Scavi and then to see its best pieces stored in the Museo Archeologico, however, many might feel otherwise. At the museum where you buy your tickets, you can sign up to see the perhaps x-rated ancient findingings in the Gabinetto Segreto/Secret Room up on the 3rd floor (2nd?.http://www.tripadvisor.com/ShowTopic-g187785-i421-k1081264-National_Archaeological_Museum_gabinetto_segreto_open-Naples_Campania.html
The Museo Nazionale is right across the street from Napoli Centro Storico/Napoli Centro. You could walk across Via Foria (street in front of the Museo) and head straight to reach Via Toledo and Piazza Dante 2-5 minutes to the left or you could go left to go up arty (perhaps by Centro Storico standards) Via Costantinopoli which eventually leads to Piazza Belllini 2-5 minutes away.
If you're in the mood to walk and want to see more of the downtown area instead of the Centro Storico/Historic District, you could just walk all the way down Via Toledo and after maybe 15 minutes (after Via Diaz and the metro construction on the left) you'll start seeing the ocean down the streets to the left once you reach the area of Piazza Municipio. You could continue down Via Toledo another 3-5 minutes to reach Piazza Trieste e Trento near the Galleria Umberto, Palazzo Reale (royal palace), Via Chiaia on the right (reknown shopping/strolling area), Teatro San Carlo (more left of Galleria Umberto), and Piazza Plebiscito. Via Toledo is a big shopping street, however, there are several reknown buildings/palazzi and churches interspersed.
It sounds like you're going to eat lunch in Pompei, however, eating in Napoli can be such an experience. Ellonway mentioned Pizza e Baba` which is in street (chairs and umbrellas set out) on the right while you're on Via Toledo a little past Piazza Dante:
http://www.tripadvisor.com/ShowTopic-g187785-i421-k1507691-Naples_Pizzeria-Naples_Province_of_Naples_Campania.html#9155699
Via Toledo after Via Diaz is blocked off to traffic, however, taking a taxi anywhere near Piazza Trieste e Trento would be a great place to be in the middle of it all. If you walk down Via Chiaia, head left along Piazza Dei Martiri, and down Via Calabritto (Gucci, Prada, Louis Vuitton, etc), you will have reached Piazza Vittoria, the ocean, and one end of Villa Comunale (the long public gardens). To head back to Napoli Centrale, you can take the #152 bus or the #1 trolley at Piazza Vittoria to Piazza Garibaldi. Napoli Centrale is a nutty 1+ minute walk in the direction of the construction:
http://www.anm.it/Upload/RES/PDF/LINEE/linea%201.pdf
A taxi ride or private driver could help you see more and get around much faster.
Buona Fortuna...