St. Petersburg is not a last-minute leisure trip. The main hassle for Americans is getting a visa. Another hurdle is getting an official invitation needed to apply for the tourist visa. And, all visitors to any Russian city must also register with the local government within three business days of arrival, a lovely holdover from the U.S.S.R. Registering is very important because failing to do so can cause problems when you try to depart Russia.
While it all sounds complicated, securing these things can be relatively easy. My husband and I had no problems getting them from our language school, but tourists will be able to get them with the assistance of a travel agency, or through an online agency specializing in the service such as Russia-visa.com or Eridan. If you read Russian, you can probably file the visa paperwork yourself, saving time and money. The perk of arranging all of the above through one agency is that they'll handle all your paperwork, as well as make arrangements for your registration once you arrive.
St. Petersburg is not a cheap city. Some of the hotels are truly five-star with price tags to match, taxis are notorious for ripping off foreigners, and a decent restaurant meal can easily cost $50 for two people. To make it more affordable, stick to mid-grade hotels, take the metro or other forms of public transportation, avoid the glitzy restaurants aimed specifically at tourists, and look for the more "local" places. For example, you can get tasty bliny with soup or salad at the chain restaurant Chainaya Lozhka (this website is in Russian only) for about $5. I almost hate to admit I know this, but you can also get a McDonald's hamburger for $1. Beer is also cheap, costing no more than $1 on the street; avoid the Irish bars if you're looking for a cheap pint as they cater to the well-heeled set and charge accordingly for their imports.
Students bearing an ISIC card receive free admission to the Hermitage, a discount at Subway (I'll admit it, I ate there a few times), discounts at many of the local Internet cafes, and much more. The little ISIC symbol is usually displayed by the counter, so even if you don't speak Russian, you can just whip out your card and reap the benefits. If you're studying in St. Petersburg and can get your hands on a Russian student ID, you'll also receive substantial discounts throughout the city at many of the smaller tourist attractions.
Unfortunately, non-students may find it harder to get discounts like these. Places like the Mariinsky Theater, famous for its opera and ballet during the colder months, still command tourist prices. In some cases this can be as much as 20 times higher than local rates. I know foreigners who regularly attended shows at places like the Mariinsky for a local discount, but they either spoke Russian extremely well or had Russian friends buy tickets for them. However, be careful with this approach as ticket collectors can smell a foreigner a mile away and will literally chase you through the theaters demanding you pay the difference.
An area of uncertainty my husband and I encountered was how to get and spend local currency. Russia is still a mostly cash economy, although credit cards are often accepted at upmarket hotels, restaurants, and shops. ATMs, or bankomats as they're called in Russian, are common and offer a good exchange rate; I usually used ones at nice hotels and never had a problem. Although traveler's checks can be cashed locally, you will likely face high commission fees and/or long processing times. I think we lost over $100 due to "fees." Hint: If you do carry cash, make sure the bills are crisp and new. I had one $20 bill that no money changer would take for fear of it being counterfeit.