As already mentioned, the big European hotels have been there for quite a while - if you go to the "package holiday" destinations like Varadero [beach], it already well and truly feels like you're not in Cuba. In fact, I hated Varadero for exactly that reason - the beach was absolutely amazingly beautiful (it is the Caribbean!), but just felt like being in an American/European resort.
Havana is certainly somewhere you want to "see" before the Americans start rolling in. It is a true 3rd world country - amazing old colonial buildings crumbling in the middle of a bustling city.
Having said all of this, the Cuban people have a very hard life - the average income is around $15 per MONTH, so it is absolutely impossible for the vast majority of them to ever even think about leaving their country for even the shortest holiday. Life won't change overnight for the Cubans though - e.g. Apple are not going to start selling iPads, as their monthly income is not going to instantly jump from $15/mth to thousands... keep in mind it is a staunchly Communist country, so the government idealistically will not let a large percentage of the population be employed by private companies. They are also very much against consumerism in any form, so it will take a long time for "true retail" to make its way in.
As for travelling there, the two best ways I've heard of are as follows:
1. the expensive way - being the way I did it! Just book flights from Mexico (mostly either Mexico City or Cancun) with Cubana (the national airline). Book return as one-way flights are pretty much the same price as return. Also, make sure you book your hotels before you get there - organising ANYTHING whilst in Cuba is close to impossible. There is no internet, people are very friendly but generally have no idea what's going on and thus are rarely very helpful. Tripadvisor Australia/US/UK doesn't have Cuba - use the Canadian Tripadvisor.
2. the bargain way - book a package holiday from Canada. I was flabbergasted at how cheap the Canadians travel to Cuba! I met a Canadian family in Varadero who paid less for their return airfares and 7 nights all-inclusive, than what I paid just for 5 nights accommodation!! Just make sure you do more than a quick day-trip in Havana... you really can't get a good appreciation from it in a packaged bus day-tour. But that's my personal view - if you like sitting on the bus with all the other tourists, not really experiencing local places, go for it!