Rome on a budget

$1800 for consumption i.e. food public transport museum, 2 people one week in Rome is enough

This sentence is a little confusing to me, " I obviously have a credit card which will be available for use if needed."

You do plan to get € with a debit card when you arrive, right? You have notified your credit and debit card provider(s) about your trip, right? You're not planning to take $ and exchange them for €, right?

Your time is short. If you haven't read the RS tips on Money, you need to do that immediately. FYI, today $1800 = about €1530 and €1 = $1.18.

Just in case your hotel has not informed you: Rome has a city tax on lodgings. You are normally asked to pay it in cash, directly to the hotel. It is not much money and will not mess up your budget, but I don't know exactly what it will cost you.

If you mean $1800 for seven days give or take, for sightseeing and meals that is more than enough. There are plenty of places where you can get a nice salad and a carafe of wine for a reasonable price. Make sure and book ahead online for sights like the Vatican Museums and the Borghese Gallery. Many of the sights take up half a day or more, and you will probably spend a lot of time walking the city and seeing free sights like churches and such. They have a transit pass that is quite a good deal for tourists, get Rick's book it will tell you all about that. I was in Italy a little over a year ago, and since last visiting in 2007 have always thought of it as an expensive country to visit. On my 2016 visit I did not find it so at all. I think the lodging part is what used to make it expensive, if you have that set you will be fine.

You have seven nights. That's about $120 per day, each, conservatively €100. Should not be a problem. You need to get to Roma from the airport and back, €15 per person each way. Then a taxi to/from your hotel, probably less than €20 for both of you with luggage.

Get advance tickets for the Vatican Museums, and the Roma Pass may work for you if you plan on the Roman Forum/Colosseum/Palatine and the Galleria Borghese (you still need to reserve a time for the Borghese, you should call to let them know you want to use the Roma Pass.

House wines are good and inexpensive with meals, soft drinks are very expensive.

With air and lodgings covered, your budget is just fine. The nice thing about Rome is that there are so many things to do and see which cost little or nothing at all! You'll have enough to cover all the usual attractions which have entry fees, though.

Getting from/to the airport (which I'll assume is Fiumicino):
The fastest way is the Leonardo Express train, which is 14€ pp and take about 1/2 an hour. If you're really wanting to pinch pennies, you can also take a shuttle bus; Terravision or SIT are good options. Either cost around 5€ - 6€ pp, take about an hour, and you can buy your tickets at the airport. Depending on where your accommodations are, it's possible you can walk or take the metro (single-ride BIT tickets: 1.5 €) to it from the bus stop.

http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-bus

As noted, the Borghese requires advance reservations/tickets so do that before you leave home. To skip long lines at the Vatican Museums, do the same; here are the links for both ticketing sites:

http://www.museivaticani.va/content/museivaticani/en.html/

http://www.tosc.it/tickets.htm?affiliate=T2C&sort_by=event_datum&sort_direction=asc&fun=erdetail&doc=erdetaila&erid=912678&language=en

I'd normally advise pre-purchasing for the Colosseum/Forum/Palatine as well but during low season, you can also go to the Palatine FIRST (ticket lines are shortest there) to get them. Once you have that ticket, you can skip the long ticket line (but not security checks) at the Colosseum. A single ticket is good for all three attractions but the Palatine and Forum are connected and must be visited at the same time, without leaving the secured perimeter.

You're going to have a wonderful time! :O)

For youngsters like yourself $1800 is more than enough in Rome for a week with air & lodging already secured. And I don't mean to disparage young folks except that they may tolerate less creature comforts then us quasi-oldsters!

It may or may not happen eventually, but a new item near the top of my bucket list is spending a winter in Rome, and budgeting that. Last March we did a week at a cheap but wonderful little apartment over a market, and for the heck of it acted like we were there long-term. Shopping at a little grocery for breakfasts and sometimes lunches, finding inexpensive locals joints for dinner, a weekly Metro/bus pass, taking advantage of a plethora of free attractions, as stated upthread.

Caffe pick-me-up a couple times a day for less than 1 Euro. Gelato for 1-2 E. Big slice of Roman-style pizza 2 E. Fifteen bus/Metro rides in a week for 24 E--no taxis or private transport. It was incredible--we were living large but not paying for it.

I didn't cost it out in the end but realized that not only was doing it the right way in Rome cheaper than most other places in Italy, it was less expensive than doing the very same activities at home here in Chicago!

It can be done...

Travelling solo for one week last February in Rome, I averaged a bit under €30/day for food/drinks/public transport/sights. I did eat simple meals, which saved quite a bit, but I didn't scrimp on the gelato or at the local pasticceria.

You have plenty of money. It always nice if your hotel included breakfast.....good start to day.
Plenty of places to have a quick inexpensive lunch. Late afternoon slice of pizza until dinner.
I usually like to have a nice sit down dinner. Of course stay away from tourist restaurants. Always great places just off the beaten path.
I always have Rick's Rome book with me.....has started up many a conversation with other traveler's. Do as much walking as you can. Many places are not that far.
I have family in Perugia. I never go without 3/4 days in Rome. Just love it.
Have a great time!
P.S. Just about everyone in service speaks English. That will not be an issue.